SOVIET QUANTUM FIELD THEORY

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• Publication Date: May 4, 1959

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SCIENTIFIC INTELLIGENCE REPORT
N? 183
SOVIET QUANTUM FIELD THEORY
1"-
CIA/SI 15-59
4 May 1959
7.) 7-, -ref
)VE
CENTRAL INTELLIGENCE AGENCY
OFFICE OF SCIENTIFIC INTELLIGENCE
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Scientific Intelligence 'Report
SOVIET QUANTUM FIELD THEORY
NOTICE
The conclusions, judgments, and opinions
contained in this finished intelligence report
are based on extensive scientific intelligence
research and represent the final and consid-
ered views of the Office of Scientific Intelli-
gence.
CIA/SI 15-59
4 May 1959
CENTRAL INTELLIGENCE AGENCY
OFFICE OF SCIENTIFIC INTELLIGENCE
-FOR-AFF46-126th-T5SE-ONL-Y-
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PREFACE
Quantum field theory is a comparatively new branch of
physics that deals with complex mathematical representations
and basic physical concepts (those of quanta and fields) in
order to explain and predict properties of the fundamental
elementary particles, such as the familiar electron and proton
and the less familiar mesons and hyperons. The former con-
cept, which held that material particles obey the relatively
simple laws of classical mechanics, proved completely inade-
quate for use in interpreting the behavior of microscopic
particles. The concept of quantum entities alone without fur-
ther refinements was also inadequate. Only quantum field
theory, which combines the notions of quanta and fields (e.g.
electromagnetic helds), has given promise of satisfactorily ex-
plaining certain physical phenomena, such as the creation and
annihilation of particles, and the existence of newly discovered
elementary particles (at present over 30 different types are
known). This branch of physics, in spite of its relative new-
ness, is marked by a rapidly growing scientific literature and
is occupying the attention of many of the world's best mathe-
matical physicists.
Quantum field theory represents the frontiers of modern
theoretical researches into the mathematical relationships gov-
erning the basic constituents of nature. As the theoretical
adjunct of experimental-particle physics, which is a large and
growing branch of modern physics, quantum field theory is
called upon to interpret and predict the results of cosmic-ray
and particle-accelerator experiments where very-high-particle
energies are involved. According to world scientific literature,
these experiments and their theoretical interpretation by quan-
tum field theory are being actively pursued in close conjunction.
Because of its very basic and tentative nature, this com-
paratively new branch of physics is confronted with many
difficulties. These are mainly mathematical problems that
involve the formal manipulation of limiting quantities,* the
nonconvergence of mathematical series, and the extension of
the region of applicability of mathematical functions into
regions that have no known physical significance. Other dif-
ficulties concern the determination of how many independent
postulates must be established, how certain newly discovered
particles should be fitted into the theory, and whether mathe-
matical rigor and correspondence with reality are possible
simultaneously.
* Limiting quantities that owe their existence to the extremely small
dimensions of the elementary particles and to the extremely large num-
bers and energies of these particles.
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The solution of these problems could lead to a revision of
present-day theories about the nature of space, time, and mat-
ter. The basic concepts of quantum field theory are funda-
mental to the physicist's understanding of nature. His mathe-
matical techniques in certain areas of modern physics, such as
solid-state physics and low-temperature physics, are closely re-
lated to those used in quantum field theory. A deeper under-
standing of the basic particles and of their forces of interaction
will be reflected in enhanced knowledge of general nuclear
phenomena and hence in the strengthening of the theoretical
bases underlying the technological utilization of the energy of
the nucleus.
The present report is based on available information from
January 1953 to September 1958. The work was carried out
under an external contract. The judgments expressed in this
paper represent the immediate views of the Office of Scientific
Information, Central Intelligence Agency.
iv
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CONTENTS
Page
PREFACE iii
PROBLEM 1
CONCLUSIONS 1
SUMMARY 1
DISCUSSION 3
APPENDIX A � Explanation of Quantum Field Theory Al
APPENDIX B � Part I � The Quantum Field Theory
Work of L. D. Landau. . . A8
Part II� Mathematical Details of the
Quantum Field Theory Work
of L. D. Landau A10
APPENDIX C � Part I � The Quantum Field Theory
Work of N. N. Bogolyubov. . A16
Part II� Bogolyubov's Derivations of
Dispersion Relations. A24
APPENDIX D � Basic Data List A29
APPENDIX E � Bibliography A44
REFERENCES FOR APPENDICES B AND C A97
TABLES
1. Number of Quantum Field Theory Papers Written by
Soviets 3
2. Number of Field Theory Papers Published in the U.S
Physical Review 3
3. Number of Top Quantum Field Theory Physicists at So-
viet Institutions and Number of Papers Published by
Them 4
4. Number of Papers Written on Quantum Field Theory
by One or More Soviet Authors 4
5. Papers Written by Top Soviet Physicists in Quantum
Field Theory Research 5
6-607 _F-OR OFF-I-G-IAE-USE-ONt'r
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SOVIET QUANTUM FIELD THEORY
PROBLEM
To assess the status and trends of Soviet research in quan-
tum field theory.
CONCLUSIONS
1. The Soviet research effort in quantum
field theory is roughly comparable to the re-
lated U.S. effort; and the work of the best
Soviet mathematical physicists who are ac-
tive in quantum field theory is quite compara-
ble, to that of the best U.S. physicists in the
,
2. The. number of physicists of "next-best"
competence in quantum field theory who
could be considered as a reserve pool of future
"beats" is considerably larger in the USSR
than in the West. Although the results of
research efforts in this field by the "next-
best" group are at present often of only mod-
erate inter* and sometimes mediocre, they
are expected to increase gradually in quality
With no loss in quantity.
3. The number of Soviet publications in
quantum field theory is increasing at a greater
rate than is the number of U.S. publications,
and in the near future will exceed the num-
ber of U.S. publications.
4. The Soviets who have been intimately
associated with the theory from its beginning
are fully aware of its general significance in
pure and applied fields of science and are
capable of making basic contributions to this
theory. In the USSR, research efforts in
quantum field theory are closely allied with
pertinent research efforts in cosmic-ray, solid-
state, and high-energy physics. The Soviets
are fully aware of the applicability of the
quantum field theory to other areas of physics
and to nuclear technology.
5. Although the Soviets are fully engaged
in work on the outstanding problems con-
fronting quantum field theory, there is no
indication of any imminent major advance
in their research.
6. Within the next decade, the Soviets
probably will take the lead over the West in
quantum field theory.
SUMMARY
� Considerable Soviet scientific effort is ex-
pended in quantum field theory. Research in
this area of modern physics requires great
Mathematical capabilities, which are possessed
by many Soviet physicists, because of the
strong traditional emphasis on mathematical
disciplines in Soviet schools. Soviet interest in
such a high-level subject as quantum field the-
ory is completely in line with the familiar So-
viet preference and aptitude for the theoretical
aspects of physical research. Many versatile
Soviet physicists and mathematicians who
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are active mainly in other areas have pro-
duced one or more papers in quantum field
theory, indicating a large potential of Soviet
capabilities in this area of modern physics.
As clearly indicated by a survey of the world's
scientific literature, a large and growing por-
tion of quantum field theory papers are by
Soviet physicists and mathematicians. Such
works regularly appear in the well-known So-
viet journals Reports of the Academy of Sci-
ences in the USSR (Doklady Akademii Nauk
SSSR) and the Journal of Experimental and
Theoretical Physics (Zhurnal Eksperimental'-
noy i Teoreticheskoy Piziki), as well as in
many other high-level physics journals, both
Soviet and Western. Many of the Soviet
works are being translated into English.
The world-famous physicists L. D. Landau
and N. N. Bogolyubov are the most outstand-
ing Soviet scientists working in quantum
field theory. Their work can easily be com-
pared with that of leading U.S. physicists J. S.
Schwinger and F. J. Dyson. Landau and Bo-
golyubov, who are extremely versatile, are
competent both as mathematicians and physi-
cists. Landau, whose name is associated with
low-temperature phenomena of s-uperfiuidity
and superconductivity and with numerous
topics in theoretical physics, has often been
called "the world's best physicist." Bogolyu-
bov's mathematical ability is comparable to
that of the late John von Neumann (U.S.
physicist). Bogolyubov's paper on dispersion
relations, important in quantum field theory,
was considered by many to be the most out-
standing paper given at the International
Conference on Theoretical Physics, held in
Seattle, Washington, in September 1956.
Since then he was awarded a Lenin Prize for
his works in theoretical physics.
Soviet physicists have been associated with
the development of the newest physical con-
cepts in quantum field theory. They include
V. A. Fok, Landau, I. Ye. Tamm, Ya. I. Fren-
kel' (deceased) , D. I. Blokhintsev, and Ye.
M. Lifshits. In 1953, A. I. Akhiyezer, who is
well known for his work in cosmic-ray physics,
and V. B. Berestetskiy did the first compre-
hensive work on quantum electrodynamics,
which may be described as an early form of
quantum field theory.
Important Soviet contributions to quan-
tum field theory include the Tamm-Dancoff
scheme, developed by Tamm; field (second),
quantization, further developed by Fok; new,
mathematical representations of Landau; and
the rigorous mathematical proof of dispersion
relations (relating to the scattering of high,
energy particles) by Bogolyubov.
The Soviets are fully conversant with West-
ern efforts in quantum field theory. They
have published papers in such Western jour-
nals as Physica, II Nuavo Cimento, and Thg,
Physical Review. Soviets who are working in
quantum field theory have appeared at 'vari-
ous international conferences and are ex-
changing preprints of works on quantum field
theory with their Western counterparts. For
example, U.S. researchers are receiving pre-
prints from the Joint Institute of Nuclear
Research, Dubna, USSR.
Many Soviet works on quantum field theory
clearly relate to nuclear phenomena observe4,
in high-energy accelerators and cosmic rays.
Such phenomena as the scattering of high,1
energy particles, nuclear forces of interaction,
spin of particles, radiation from fast moving
particles, and creation and annihilation of
particles are often discussed. Bogolyubov,
the chief Soviet worker in quantum field
theory, is the head of the Laboratory of The-
oretical Physics at the Joint Institute of Nu-
clear Research, where the world's largest par-
ticle accelerator � 10 billion electron volts
(Bev) � is located and where extensive eXy-
perimental research on all phases of high-
energy particle physics is being conducted.
This indicates close cooperation between the-
orists and experimentalists at this ' center,,
Most of the authors of the quantum field the-
ory papers are doing research related to
cosmic-ray and high-energy physics at well-
known Soviet universities.
Soviet physicists are pursuing research ifl
quantum field theory along two main
The first, an older one, involves field equa-
tions and perturbation methods, and repre-
sents a direct outgrowth of the still ,014,
quantum mechanics. The second and ftewef
approach, which involves so-called ationla
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factory features of the first approach, deter-
mina the ultiMate. Mathematical properties
Of the, genera field equations by gradually
restricting their generality trough the im-
position, Of certain mathematidal Condition,s
(axioms) corresponding to. physical reality,
such etry and casuality conditions.
These two aPproaches are ].clbtely associated
with the, Work ,of Landau and Bogolyubov,
respectively_ 111 some cases, pertinent studies
were initiated in the West and further devel-
oped in the USSR. In other cases, studies
were initiated by Soviets and carried further
by. Westerners. In general, Soviet and West-
ern research in quantum field theory closely
parallel each other and rely on one another
for ideas and clarification. There are as yet
no indications of any radically new develop-
ments in or departures from present trends in
Soviet and Western quantum field theory re-
search.
DISCUSSION
On the basis of the detailed data in ap-
pendices D and E, tables have been prepared
tO show the quantity of work that has been
dale it quantum field theory. Tables 1, 3,
4, and 5 represent Soviet activity, and table
2 summarizes U.S. Work.
TABLE 1
NUMBER OF QUANTUM FIELD THEORY
PAPERS WRITTEN BY SOVIETS
)30CIRE EARLY
* '1953 1954, 1955 1956 1957 1958 Total
44 51 49 91 128 91 11 465
* 'Before 1953" indicates the number of papers
that �Imere,,published before 1953, but they were not
reviewed or abstracted until after 1953.
TABLE 2
NUMBER OF FIELD THEORY PAPERS PUB-
LISHED IN THE U.S. PHYSICAL REVIEW
EARLY
1953
1954
1955
1956
1957
1958
Total
91
102
114
93
93
56
549
(61)*
(68)
(76)
(62)
(62)
(38)
(367)
. *Figures in parentheses represent the articles
that are on the type of research considered in this
report.
Table 1 presents the total number of pa-
pers published by the Soviets in quantum
field theory. The papas have been located
through a survey of the Soviet literature.
Table 2 gives a comparable breakdown for a
typical U.S. publication, The Physical Review.
The figures of table 2 can be compared with
those of table 1 only in a very rough way.
They represent the number of articles listed
under field theory in the subject index of The
Physical Review. The term "field theory" as
used by the Soviets has a much broader mean-
ing than U.S. usage and includes many arti-
cles that might more properly be placed un-
der another subdivision. In table 2, only
about two-thirds of the numbers listed (those
in parentheses) would be articles on the type
of research considered in this paper. The
figures in table 2 represent the papers in only
one U.S. journal in which U.S. scientists pub-
lish research in quantum field theory, but
this journal publishes a large percentage of
the U.S. reports in the field.
According to tables 1 and 2, the quantity
of Soviet work in quantum field is about equal
to the U.S. effort alone, although probably
less than the total Western effort, especially
if Japan is included.
Table 1 indicates that the Soviet effort is
growing at a more rapid rate than that re-
flected in table 2. The Soviet papers of 1957
and 1958 are still being translated and are
not all included, so that those numbers in
table 1 will be subject to revision upwards. It
is believed that this rate of Soviet growth is
probably a real one, not reflecting simply the
increasing availability of Soviet works. If
this rate continues, the quantity of Soviet
work in this field will probably equal and then
exceed the Western effort in the near future.
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TABLE 3
NUMBER OF TOP QUANTUM FIELD THEORY PHYSICISTS
AT SOVIET INSTITUTIONS AND NUMBER OF
PAPERS PUBLISHED BY THEM
INSTITUTE
NUMBER OF PUBLICATIONS
No. of Before
Physicists 1953
1953
1954
1955
1956
1957
Early
1958
Totals
Moscow State Univ
33
12
13
11
13
26
19
4
98
Physics Inst imeni
P. N. Lebedev, Acad
of Sciences, USSR
19
2
4
6
18
14
12
4
60
Various Institutes
of Physics of the
Acad of Sciences,
USSR
18
2
4
6
18
14
12
4
60
Leningrad State
Univ imeni
A. A. Zhdanov
11
3
1
6
9
7
4
3
33
Joint Inst for
Nuclear Research
13
1
6
6
13
Inst for Nuclear
Problems
8
1
1
3
3
6
7
1
22
Totals
102
20
23
32
61
68
60
22
286
Table 3 presents data pertaining to physi-
cists and institutions. In some cases, authors
publish from several institutes. In other
cases, it was not possible to ascertain the au-
thor's institution. Thus, the table presents in-
complete statistics and only represents a
trend. Furthermore, the Academy of Sci-
ences, USSR, is not strictly an institution, but
many papers are published with its designa-
tion. The tabulation indicates that there are
only a few institutions of dominating impor-
tance both in quantity and quality of their
output.
TABLE 4
NUMBER OF PAPERS WRITTEN ON
QUANTUM FIELD THEORY BY ONE
OR MORE SOVIET AUTHORS
NO. OF
Auritoss
No. or
PAPERS
1
342
2
95
3
26
4
2
5
0
4
Table 4 presents a breakdown of the Soviet
work by number of authors. The number
papers with only one author exceeds the man
ber of those with more than one. Some Atti
very best men, e.g., Landau and Bogolyuixif,
almost invariably publish with others in
field. Their counterparts in the United
States, Schwinger and Dyson, almost, in
ably publish alone, but many very good playa
cists in the West also usually publish *tki
e.g., T. D. Lee and C. N. Yang. The 'QV _
percentage of single and multiple a_
ships is probably about the same for the
viet Union as for the West.
Table 5 lists the top producers of mere
quantum field theory, and the numbers of
pers are a fairly good reflection of the gene.
relative importance of the men in this osin
of physics. Some of the men, for WW1
Pomeranchuk and Landau, are more prod
tive than the numbers of publications'
since they also do a great deal of work lit
areas of research.
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'TABLE 5
PAPERS WRITTEN BY TOP SOVIET
PHYSICISTS IN QUANTUM FIELD
THEORY RESEARCH
No: OF
PAPERS
24
20
16
'15
15
14
12
12
11
10
10
10
Total 187 14
AUTHOR
Bogolyu.bov, N. N.
Sokolov, A. A.
Ivanenko, D. D.
Shirokov, Yu. M.
KhalatnIkov, I. M.
Fradkin, Ye. S.
Galanin, A. D.
Abrikosov, A. A.
Medvedev, B. V.
Landau, L. D.
Novozhilov, Yu. V.
Pomeranchuk, I. Ya.
Zaytsev, G. A.
Barashenkov, V. S.
Moreover, there are about 200 additional
then (see appendix D) who have written only
a few papers on this subject. In all, this rep-
resents a large reservoir of potential workers
in the quantum field theory, who presumably
at present are Working in other branches of
science.
The number of physicists listed in table 5
who might be considered the best in the field
is smaller than a comparable list of Western
physicists would be. On the other hand, the
hat of physicists in appendix D, which in-
cludes men who probably work in other fields
of science, but who still have published in
quantum field theory in the last 5 years, is
perhaps somewhat larger than a comparable
Western list would be and presumably will
grow in the future. This latter fact repre-
sents a significant difference between the
USSR and the West, or at least between the
USSR and the United States, in attracting
young scientists to this field of research. In
the last 5 years or so, the West has been dis-
couraged with the difficult problems of quan-
tum field theory. As a result, fewer good
graduate students have been encouraged to
enter this field. Students have probably been
reluctant to enter this work in the United
States because of the mistaken impression
that such recondite research is not as reward-
ing financially as other less fundamental
work might be.
The total number of men qualified to work
in this field is probably about the same in the
United States as in the USSR. The Soviets
appear to have produced many new workers
during the last few years. Financial support
for this type of fundamental theoretical re-
search may be obtained more easily in the
USSR than in the United States.
The overall type of research in quantum
field theory done in the USSR is much the
same as in the West. They have worked in a
large number of different areas in quantum
field theory, with only a few of particular
interest.
The Soviets seem to be doing quite a bit
of work in the area of the strong-coupling
meson theory. They have attempted to work
out such a theory for w-mesons (the mesons
of interest in nuclear-force problems) with-
out too much success. Some work along the
same lines has been done in the West, but by
and large, the feeling has been that such an
approach to the nuclear-force problem was
too much like perturbation theory 'and would
not be too fruitful.
Another such example of comparative So-
viet concentration is the application of the
Tamm-Dancoff scheme of approximation.
This is related somewhat to the strong-
coupling theories. This scheme represents a
slightly different approach to perturbation
theory, wherein the quantities of interest are
not expanded in powers of the interaction,
but rather in the number of particles in the
intermediate states. Of course, it is natural
that much of this work is being done in the
USSR, since Tamm was one of the founders
of this technique. Again, quite a bit of work
along these lines has also been done in the
West, notably by Bethe's group at Cornell
and by Dyson at Princeton. In recent years,
this method has been virtually abandoned by
the West in favor of other approaches.
One such Western approach to the nuclear
force problem has been that of Chew and Low.
This was originally a semiphenomenological
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attack on the problems of low-energy w-
meson scattering data. By the use of this
approach, Western scientists were moderate-
ly successful in correlating these types of ex-
periments, and were particularly successful in
explaining the resonance behavior observed
in w-meson-nucleon scatterings. Subsequent-
ly, the approach was refined to the point
where it became of more fundamental in-
terest, because many of its ideas and conclu-
sions were of a more general nature than
they were originally thought to be. These
early successes of the Chew approach, and
the subsequent theoretical refinements by
Low, Wick, and others contributed a great
deal in reviving the somewhat flagging in-
terest in quantum field theory.
Very little, if any, work on the Chew ap-
proach has been done in the USSR. This is
probably just a counter-example to the West-
ern reaction to their work in strong-coupling
theory, or, more appropriately, to the recent
work of Landau. A great deal of work on the
Landau approach has been done in the USSR,
whereas almost none has been done in the
West. Western physicists have felt that this
approach contained basic mathematical er-
rors which made its results inconclusive. Not-
withstanding this Western reaction, many
Soviet papers along these lines continue to be
published.
A final point to be considered here is a
general impression concerning the level and
effectiveness of Soviet training in this field.
This, of course, can only be an impression,
based on a few text books, their general work,
and some conversations with physicists who
have visited the USSR.
In general, the level of training in the
USSR in field theory seems to be very high.
For example, there seems to be official sup':
port or encouragement for their best workers ,
to write textbooks. These textbooks are writ, (
ten and published very quickly, so that they
have timelY. interest. Since they are written'
by top men and reasonably priced, they prob.,
ably are influential in enticing young worker
into this field and in retaining those who are.
already in it. Just within the last few years,
the following books have been written: Quart;
turn Theory of Fields by Bogolyubov and
Shirkov; Quantum Electrodynamics by Akie.1
zer and Berestetskii; Foundations of Qua*
turn Mechanics by Blokhintsev; ClassiccC
Field Theory by Ivanenko and Sokolov; C/a.s,
sical Theory of Fields by Landau and Life
shits; Quantum Mechanics' Non-Relativistic
Theory by Landau and Lifshits; and Proto,
lems in Dispersion Relations by Bogolyubov
Medvedev, and Polayamov.
The books themselves, or their proofs or
translations, indicate that not only are the
written by the best men available, but, as
textbooks, they are generally excellent. As a
consequence some of the very best books
field theory available in English or German
are translations of these Soviet works, man
published by American houses. Thus, thes
books are becoming standard and in many
cases they are the only textbooks in this fiel
in many American universities, notwithstand
ing the high cost of the translated versions.
The particular quality of some of the bett6
Soviet work in quantum field theory is bes
illustrated by the work of Landau an
Bogolyubov, which represents the only lines
-Of Soviet research of special importance dur.4
ing the past few years. (See appendices )1.
and C.)
6 _EDR�Ord-r4G-I14L--15SE�CFNEr
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12011--9141P-I-eLest�ME-011L1�
APPNNDIX, A
LANATIoN OFOANTLiM FTETD 112,C)RY
� Basic research in Modern Physics can conveniently be broken down
into. sUbdiVisions or steps according to the size of the object under
stay. . The, first step is the study of very large objects -- the universe
,a0 a Vidlial including the galaxies, stara, and planets. Studies 'on
the universe lean heavily on the ideas of special and general relativity,
etohydrOdyflamics, classical mechanics and thermodynamics.
The next step is the study of matter in bulk of every-day size.
IL is, the physics of solids, liquids, gases, and plasmas. In the
last few decades, this phase of physics has made tremendous strides,
as evidenced directly by the sudden growth of advanced technologies.
The great strides in the fundamental understanding of the properties
of matter in bulk can be traced to contributions originally made in
the study of the next smaller stage. .
The third step embraces the constituents that make up matter in
bulk -- the, molecules and their constituents, the atoms. It was at
this stage that the revolutionary ideas, of quantum physics were first
found necessary and introduced in the early decades of this century.
These ideas and theories, linked with scientists such as Bohr, Planck,
NinaliMa.A and Dirac, have gradually permeated physics, until today,
the concepts of quantum theory are considered fundamental to under-
ing of ,nature , in general. Not only have these concepts filtered
to the next higher step, the study of matter in bulk, but they
lead directly to the next lower step, the study of the elementary Particles.
Thus, the ideas of quantum theory must be used in the 'study of
'Constituents of the atoms themselves, the protons, neutrons, and
electrons. In attempting to understand the interactions between these
fnillamental "building-blocks" of matter in the universe, and their nature
and structure, the most modern versions of quantum theories must be
called. into play.
The fundamental particles and the various interactions between them
are described in terms of quantized fields, so that there is a one-to-one
correspondence between a quantum field and a particle or family of
particles, such as the proton and neutron. The interaction itself, for
example, between two neutrons, is represented by another quantized field,
which in this case corresponds to another real particle, first predicted
by Yukawal the 'fl'-meson. It is the study of these various quantized
fields and their behavior under different conditions that is called
quantum field theory.
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Still another way to place quantum field theory in relation to the
rest of theoretical physics is to consider the energies involved in the
interactions or forces between the particles making up molecules, atoms,
and nuclei.
The unit of energy generally used in discussing atomic and nuclear
physics is the electron volt. This is defined as the energy acquired by
� one electron in falling through an electric potential difference of one
volt. The thermal kinetic energies that molecules in the air have at
ordinary temperatures, just for their random motions, are about one-fortiet4
of one electron volt.
The interaction energies between ions or molecules in a solid* is
about a few tenths to a few electron volts. This is the same order of
magnitude ds those energies that bind the constituent atoms of molecules,
and represents the energies of general interest in bhemistry.
The energies invOlved in binding the electrons within the atom itself
range from about tens of electron volts, in the lightest elements, to
some thousands of electron volts in the heavier elements. It is this
order of magnitude of energies that is involved in atomic transitions
responsible for the emission of light in flames or light from the sun
and in the emission of X-rays in a X-ray machine.
On the next level, within the nucleons of an atom, the interaction
energies are very much larger, and are of the order of 10 Nev. (million
electron volts). This is why so much more energy is released in an
atomic explosion, which involves the release of these interaction energies
compared with a chemical explosion, such as TNT, which involves the
molecular interaction energies.
All of the energies except the nuclear are quite small compared
with elementary particle rest-mass energy, i.e., that energy Eto which
the mass in of a particle corresponds in the Einstein relation, g'.:=4,7ci
The rest-mass energy of an electron is one-half Mew; that of a`yr-meson,
140 million electron volts; and that of a proton is about 1 Bev. As
long as the interaction energies are very small in comparison with the
rest-mass energies, so that there is no question of having enough energy
to create new particles, quantum field theory is not generally used,
although ordinary quantum mechanics is. When the interaction energies
become so large that elementary particles might be created, as they do
in the nucleus, then quantum field theory is essential, for it treats
these interactions not so much in terms of indivisible particles, but
rather in terns of fields wherein the number of particles can change by
creation or annihilation.
*The strength of these energies determines whether the substance
Is a solid rather than a liquid or gas.
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us quantum quantum field theory is necessary in that region of energy
141 foom about 1 million election volts (creation of electron
throw* nuclear energies of 10 to 100 Mev to the highest
Aildbls.' These are from high-energy particle accelerators* and
&side -lays.** At these energies, all sorts of particles are created.
se iholude some, ,called K.-mesons, whose mass is between that of
t7-meson and the proton; others called hyperons, whose mass is
Ater than one proton mass, but less than two proton masses; and
erhapp as yet undiscovered new particles.
Quantum field theory can be divided into two approaches(l) the
older approach involving field equations and perturbation theory;
. and (a) the new: or axiomatic approach.
The older approach was a direct outgrowth of the even older
(about 1920-30) quantum mechanics. This approach attributes certain
mathematical functions called wave functions or fields to such
physical entities as elementary particles. These fields are assumed
to Obey' certain mathematical equations, the form of which is
determined by certain physical properties of the fields realized in
nature - for example, its equations are Lorentz-invariant and have
certain symmetry Properties. The physical interaction between
various particles (e.g. the Coulomb interaction between electrically
charged particles) is described by a certain mathematical combination
of the field functions of the interacting particles and this inter-
action term is inserted in the field equation in the appropriate place.
Thus the field equations, with the interaction terms, could be
written down directly and should determine the form and behavior in
space and time of the field functions. With the determination of
these field functions, it is possible to calculate such interesting
physical quantities as the energy of interaction between two inter-
acting particles, such as two protons in a nucleus; scattering cross-
sections, which are a measure of the probability of one particle
scattering from another in a certain way in experiments that could be
performed with high-energy accelerators; the life-time of unstable
particles; the internal structure of such elementary particles as the
proton; and many others.
While the field equations can be written down, their solutions
can not, in general, be obtained. Only approximate solutions are
possible, in practice, and these are obtained by an approximation
procedure called "perturbation theory." This mathematical technique
consists in first obtaining solutions to the field equations when
the interaction term is neglected. This corresponds physically
*About 10 Bev' Wherein proton pairs are created.
**Extremely high energies from a thousand to a million Bev.
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to assuming the neglected interaction energies are quite small in
P
comparison with other relevant energies, such as the Itinetic energies.
to phys
Having this "unperturbed" solution, one finds corrections to it in
t
which the interaction is allowed to act only once (first-order
Inwhich cert
perturbation theory). Corrections to this correction are then found,
relatio
in which the interaction acts twice (second-order perturbation theory),
reflect
and so on.
hoped t
will co
One of the decisions to be made in quantum field theory is whether
field f
or not such a perturbation-theory approach to these equations' solutions
is valid. In. using this approach, it soon became clear that it was
formally meaningless. Mathematically infinite quantities appeared in
the equations. A successful but not entirely satisfying method was (1
developed for removing these quantities in the "renormalization" ,
program when it was noted that they always appeared in relation to a (2
few fundamental properties of the field, like its mass and charge. suitabl
Thus, the original or ''bare" mass and charge of the field put in the
equations could be combined with these divergences to give, by
definition, the real, or renomalized mass and charge of the particle.
Actually, the equation changed the character of the so-called vacuum , (11
from being a state of nothingless, so to speak, to a quantum mechanical present
state in which no real particles were present, but in which virtual
particles could continually be created and destroyed. Thus, in going T1
from a particle's "bare" charge to its real or "renormalized" charge, diffict
the particle has essentially interacted with this vacuum in such a way
that virtual pairs of particles surround it and alter its original 9R
charge. The prediction of this type of strictly quantdm field- 'mobilo]
theoretical effect, confirmed by some extremely accurate experiments,
was one of the great successes of quantum electrodynamics. T1
out thE
Nevertheless, although these effects are observed, the fundamental procedl
mathematical structure of the theory is still very unsatisfying. limits
integn
In an attempt to by-pass these unsatisfying features of quantum
field theory, a fairly new, axiomatic, approach has started to
develop. This approach does not use field equations and the strictly 4944tb
dynamic properties of fields, but rather attempts to speak very
generally about the ultimate mathematical properties that the field
functions, or certain combinations thereof, must have.
Thus, certain physical properties of nature, like Lorentz-
invariance, causality (roughly: no signal traveling faster than light,'
or no output before input), and certain invariances in space and time
are translated into mathematical terms. These properties are 'Used as
restrictions on the functions themselves rather than to determine field
equations that the functions must satisfy. This provides a very broad
class of mathematical functions. Then, one by one, restrictions are
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placedLon these functions by means of the basic axioms (which correspond
I-644;031dd', properties). These restrictions are represented by equations
*huh -the.fOtetiOns must satisfy, entirely different from field equations.
In certain instances, the restrictions lead to equations called dispersion
relations. If If a-set,of restrictions that are an exhaustive and accurate
reflection of nature can be successfully placed on these functions, it is
444(i:that:the. set. of. that are left will be BO limited that they
will '0.0P$tittte an: answer to the original problem of obtaining mathematical
field functions to represent the physical world.
The following questions still need to be answered:
(..]) Can a Set of restricted functions be obtained?
,
.(2). Ira set of restricted functions is obtained, will they be.
sPitSble?
(3) Are the axioms really restrictive?
,
- (4) Are.,the axioms mutually contradictory? If they are the
present concept - of nature must be changed. -
'2514,4 both.approaches in quantum. field theory.are beset by severe
difficulties and. require further research
-
-There have been several severe criticisms of this method, Which,
probably accounts for the lack of Western interest In the Soviet work.
.,e first few, general criticisms, are made by Dyson. 16/ Be points
out that there is. no justificatiOn,'mathematicallyl-for using cut-off
procedures 'Especially Mapecially in the two-cut-off case, the method of taking the
' limits is arbitrary Whether one can interchange- limits like this' with
integrations is unknown.
, The problem of the singularity in the proton propagator is shown in*
He404tion 15, appendix B1 part II. This appears At a momentum of
e31/a. m2 e1000m2
'Stich is extremely high, but finite.. What this means physically is not
clear. In the case of the mason, theory, equation 14, this singularity
-qpiears at experimentally observed energies NI, where M is the nucleon
mass. Besides this, the analytic, form of equation.15 means,that,there
a. double "ghost" state in the. Lee model sense, a residue of the wrong
*All equatioins referred to in this section are in appendix B, part Ill
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sign, and at imaginary mass values. Again this seems to make for
problems in physical interpretatioie.
Still more severe criticisms of a mathematical nature are made by
Kallen. 11/ These criticisms are based on the approximations mentioned
with reference to the eqpation for the vertex function, equation 6, and
its solution. It is still not clear 'what effect the terms neglected
there might have. In solving equation 6, one expands the integrand in
a perturbatiowsum, integrates, and then takes the sums of the series
again. For integrating, cone repladealtha-torma:,bassunieVasyMptetic
forms, and then assumes that the sum of these asymptotic terms is really
the asymptotic limit of the original sum. There is always a cut-off.
It is expected that a highPr-order process does ntt become important
until thelenergy is well above its threshold. Thus, for a given cut-off
energy, the asymptotic value for a process is being-assumed in an energy
region where the process might still be small. In other words, if a
given cut-off in the integral eliminates processes whose thresholds are
above the cut-off, the resulting sum of integrated expressions is a
limited one. When the cut-off then goes to infinity, asymptotic
expressions for processes that have already been excluded should be
included. Thus, the expression for the sum may not at all be its
asymptotic form. Perhaps this explains why the presumably divergent
sum of divergent terms gives such simple, convergent results. Kellen
approaches the problem of summing the series of asymptotic terms from -
a different point of view, i.e., at high energy, a process is a multiple
of the corresponding Born approximation. Be gets an answer entirely
different from that obtained. by Landau and his co-workers.
The work in quantum field theorylay-LablauHand his co-workers appakl
to be,opet to very serioUS questions on, rigorous mathematical grounds',
This should not be taken to imply,' however, that this is true, in gener4)
of Landau's work. Landau is probably one of the best physicists in the
world. While work on quantum field theory is open to questions, it had
the positive effect of again stimulating thoughts on these subjects
throughout the world. Thi6 probably led to some of Tallenls more recent
work as well as to some of the ideas in the axiomatic approach to qm*4001
field theory.
In addition, Landau tea made very significant contributions ialaanl
other fields. Most recent, and perhaps most spectacular, of these 14440
work on the two-component theory of the neutrino-1 and its connection �
with the parity experiments. 'Before that, he did very early and. good
on the properties of liquid. helium. Be has contributed 'significantly.,
the theory of multiple production Of mesOns in cosmic rays. There are
other examples. Thus, this analysis of the TAndau approach to qpant0
field theory should be taken merely as an example of one of many aPPrO.$
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while there are some questions as to the validity of this approach,
it has not been proved. incorrect. It may not be an example of Landau's
better work, but it does demonstrate his versatility and. the influence
by that his work has on other Soviet work.
oned
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APPENDIX B
PART
THE QUANTUM FIELD THEORY WORK OF L. D. LANDAU
Fbr many years, the problems of divergences plagued the
perturbation approach to quantum electrodynamics. If certain simple
-atiobe were computed straight forwardly, such as the effect of
an electrdn's self-energy (mass) because of its interaction with the
e/ectromagnetic field, mathematically these corrections were infinite,
rather than: mall, as they should be.
In 19471, Kramers observed that all such corrections to the mass of
an electron, while they might formally diverge, were still only to be
�
�erpreted as changes in the particle's mass. Since a mass is observed
^hreienliy, presumably of the electron interacting fully, the fictitious,
original free electron mass together with all its corrections should be
identified as the true, observed. mass. Thus, these divergent quantities
were to be absorbed with the original electron mass, and the result
defined as the ueual finite observable mass. This is the basic idea
behind the renormalization program in quantum electrodynamics. When
similar ideas were applied to other quantities, like the electric
charge, it could be shown (see Dyson) that all divergences were thus
removed from quantum electrodynamics. Similar considerations hold for
some forms Of 'meson theory: H. A. Bethe and F. de Hoffman.
� With this successful removal of divergencies by renormalization
and the subsequent experimental confirmation of the very precise
theoretical predictions, it was hoped that the inconsistencies had
been removed from quantum electrodynamics. It soon became clear that
whether or not they had been removed was still open to question.
T. D. Lee gave a good example of a theory which could be renormalized
ami in which the S-matrix* is nonunitary. 4/ 5/ Such a situation
corresponds to a physical situation in whicE gates of negative probability
occur; hence it is inadmissible.
�.Still another matter that had to be determined VW the rather formal
ote of the nature and source of the divergences removed by renormalization.
The problem was to determine whether these multiplicative constants were
Ufinite because of an unwarranted usage of perturbation theory (e.g. the
Perturbation series perhaps diverges)* or whether the 1.nfinities itherent
in the theory wereitdepmdettofperturbation series expansion.
*S-matrix - The scattering matrix - the quantity that contains )1 the
information of the theory on scattering processes.
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Kallen and. Lehmann showed that at least some of the renormalization
constants were inhPrently infinite. Thus, there still remains the
question of the origin of these infinitiez!.L2t.gell-Mann and Low have
attempted to investigate the high-energy (or,-equivalently, very small
distance) aspect of the functions involved in quantum electrodynamics,
using perturbation theory as we].], as some.group,properties of these
functions. 9/ Their results, while interesting, were rather inconclusive.
Recently, foigolyubov has refined the group theory approach to this matter,
without essentially changing its inconclusiveness., 10/
Throughput these more recent doubts. as to the inconsistency of
electrodynamics, there has long been the question concerning the
connectionl)between the point-like nature of the interaction assumed in
electrodynamics and the infinities that arise.. It' was felt that, while
this problem was still somewhat puzzling, po fUndamental(questions were
involved..
In quantum electrodynamics, this question of point interactions, of
course, corresponds to very high-energy asynptdic behavior of the relevant
functions. This whole question was reopened by Landau, who used a
potentially very powerful technique not necessarily restricted to a
perturbation-theory approach.
..,The approach adopted ,by TAndau is based on the field., equations'
deriVed by Schwinger and Fradkin. 'In principle, these equations
exact and independent of perturbation theory. In practice, certain
approximations must be made in order to solve these equations and these
approximations depend strongly on a perturbation approach This approach
gives much the same answers and conclusions for the meson'theortrand even
for beta-decay. types of coupling. The. physical .coupling vanishes in the.
point-interaction limit..
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PART II
::MAIMSVATiCA) DEUIT.A.PF TBE QUANTUM FIELD 11.41071 WORK OF L D. LANDAU
labia work on quantum field theory, L. D. Landau used several field
One to determine "Green's functions." In this context, a Green's
function* contains all the information necessary to find the behavior of
the electron's wave function in space and time; i.e., in principle, it
contains the information necessary to answer questions about scattering
and ether problems. The term "propagater" is used almost interchangeably
with the term "Green's function." nais usage reflects the fact that
this function i contains the information on how the particle propagates in
ewe and time (or, more strictly, the Fourier transform of G(p) does).
As an example, the Dirac equation for a free electron in momentum
evade in terms of the corresponding free-electron's Green's function,
(p) is given. This is
0146' e(V) - mij
1
where, mt. is the electron's bare (in this case actual) mass. This equation
is reallraymbolic, in that it is a matrix equation as well as a
differential equation. The symbol 1) stands for the four-dimensional
Beelar product where the four-vector Y's are the Dirac matrices.
/t is clear from equation 1 and the above explanati8n that there is
,a6 term in equation 1 referring to interaction (hence, G (p) is designated
as :the "free" propagator).
If the electron is allowed to interact with the electron-magnetic
field, then Schwinger's exact equation for the electron propagator becomes
2. o(ri�fi: G-(p � k)7iry Ivy (k)dJ=I.
z rn(i)
In equation 2, the third term in curly brackets is the effect of the
electromagnetic interaction. e, is the bare electric charge (this equation
� Is, of course, unrenormalized). c is, as before, the Dirac matrices.
p( P, P-k; k) is known as the vertex function; it contains the information
cdicerning the form of the interactions, and is to be determined from its
equation.444# (k) is the photon's Green's function, and it, too, is
determined by its equation. It is also clear from equation 2 that we now.
-*For-the electron, this is-denoted as G.(p),.e function of the electron's
four-momentum P.:' - �
**The summation convention on four-vector and tensor indices is used in
all of these equations.
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deal with complicated matrix equations of the integro-differential type
(the differential operators in space-time being here just P; the integral 1
equatiOn form coming from the(p-a) Under the integral).
The corresponding equation for: the photon propagator D (k) is,
fAV, TrA,
. 0
Here, I)Itc� (k) is the "free", soninteracting photon Green's function,
analogous to G�(p). Thus, where G�(p) satisfies the free Dirac equation
1, and has the solution
Dpv�(k) satisfies the free Maxwell equation, and has the solution
0
5. al,tv e
The operation Sp means that one should take the spur, or trace, of the
matrix quantity in the square brackets.
Finally, the equation that Landau uses for the vertex function is
6. r; (F)T.-4; 7=--
YG--1-_4: jr-t1(-?_k) k) 6_07_ k)
This equation is the most complicated of the equations 2, 3, and, 6,
because it is a matrix, nonlinear integral equation. It is nonlinear
because the unknown function F. (--) appears more than once under the .
integral.
� In all. evations, it is sometimes useful to think in terms of ,
Feynman graphs. In a very rough way, these graphs show the electron
and photon propagating in space-time. The electron is indicated by a
solid line and the photon by a broken line. When G(p) appears, it
� corresponds to an electron; when Doily (k), appears, it corresponds to a
photo-n; � when /(--) appears, it corresponds-to a point of interaction
between them; and1)/z7/�(k) or G�(p) corresponds to propagation with
no interaction.
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kictron (photon) is complete with interaction, G(p), CD
'Voltd (broken) lines are double. When the vertex is the
one, 41(--)1 it will be. represented by a circle at the line
dna.' When it is only the 'bare" interaction, it will be just
section: Thus, 'equation 3 can be graphed as follows:
nation 6 may be
, I'
11
i
� = =
graphed as follows:
i
11
in Clear from graph 8, that other possible topographidal forms
� excluded, for example
9.
e original equation of Schwinger includes these graphs and all other
Neglecting these is the approximation mentioned above'.
that landau makes ln-SChwinger's equations
In al] these equations, the integration variables (say pror-k)
-0PrreiVond'to'the energy-momentum of intermediate-state particles (in
terms of graphs, the internal lined) The investigation of the effect
or point interactions is introduced as follows. The original interaction
between the electron field and the electro-magnetic field was 'considered
to Occur at a mathematical point in space. This restriCtion is dropped,
and it is considered that this interaction takes place ip a small region
Of Space-time, say of dimension :a (presumably about 10-17*.to 10-1
centimeters, from present-daynxperimentn).- In these equations., which.
are in mamentum-spacel, this spread corresponds to an upper limit on the
intermediateetate particlestMomenta, i.e., the integrals in the above
equations are cut off at an upper limit of momentum, of the order of
1/a. Thus these integrals are made finite. It is hoped that when
a calculation is completed, the limit a-4o, orA-*ool will correctly,
correspond again'to.a point interadtioni and, in passing to this limit,
Something will be learned of the divergences. Thus; landau's program
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is an attempt to solve the einilltaneousintegrp-differential equations
2, 3, and 6; incorporating the upperlitit on tie integrals, and then
passing to the point. limit'..
Since the divergences that occur in the perturbation solution of
these equations are logarithmic with momentum: the major contributions
to the integrals cone from, the '..high intermediate momenta. It is ,
because the divergencies are logarithmic that Landau uses equation 6
rather than the complete equation. He feels that this equation contains
all the terms contributing importantly to the divergence.
To solve these equations Landau assumes that when the momentum
becomes very high, the Green's functions assume certain simple
asymptotic forms.
10.
[74 cp,i;4 yt,to< (f)
k ko (k\
11Zz[61t0(2)(Spv
where f2 is any p2 0 q2 1 12 if they are of the same order of
magnitude, and, if not, shauld be ,the largest. The functions of
,cK ,dt and di, are slowly-varying function of their
arguments.
Substituting these expressions in equations 2, 3, and 6, he
solves for the functions. In doing so in the, equation fo 1j.4,(p; p4E;
Landau mAli.es an additional assupptionln. finding the dependence
on the second variable p when it differs from o in comparison with :k.
This is, that in finding the_change in -1T4(....) in going from p=o-ta
smAll p, he can consider:the changes in. the integral in equation.6 00
the smut the changes of the. integrated expressions.
As solutions to these equations, Landau finds that within the
approxinations made.in.writing down equation .6, the functions
can be chosen as 1; i.e., there are no, corrections to the electron..
free Green's function or to the "frpe7 vertex function & . However,
the photon propagator is changed from its free value of dlt== 1 to
11.
III n
.e1' is the bare, unrenormalized electric charge....-. To, put the
propagator in repormalized terms,_it.phst be written, in such a:wdy
that it. does not depend on the unphysical quantities -e12 and the,
cut-off To do this, the real, observed electric charge e`
(=I/137) is defined in terms of e12 in the following way:
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oelv in . the cpwork scattering of,zero-energy,.photons (or,
--$4y044:� that Coulomb's law gives the potential between two real
t44:11.40,41.5*ncee). When equation 12 is used in equation II,
al6ging, equations result:
13.
2
+ 022)
ez
2
at0:2) = e �
ez
9-rr VY1')
2, 2
and thUS,'if we multiply dt(k2) by the renormalization constant el /e,
the'renOrtalized propagator does not depend on any unphysical quantities.
in all these equationsl.the point interaction limit is taken by,
letting. Originally, Landau aseumed that the bare charge2e14E4: I.
From equation 14, it is clear that asik5 increases, eventually el!>>. 1.
This difficulty is eliminated by Pomeranchuk, who introduces two cut-offs,
0110 for the intermediate bosons (photons)-kk, and one for the intermediate
fermiOns (electrons)4p, and
I/ Results similar to those in equation 13 are obtained.
The conclusioas to be drawn from equation 13 is somewhat Startling.
Rm., as long as el'XO (necessary for unitary S-matrix), irrespective
,11. the varipon of e12 ItithAy we have the limiting conditions: as
- ../V+00 e 0. Thus, choosing a point interaction corresponds
to no physical interaction at all.
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This work' has been followed by Many works in the USSR that apply
the same analysis to other theories. 1/
It is essential to remember that in this analysis,Arepresents an
upper limit to the momenta. If, for example, the photon momentum k>>.A. ,
then Landau finds 17t4w0,1/2-�-oo rather than /i; = yiz . This is as it
should- be, because as the energy becomes very lafge, it is expected
that the effect of the (presumably) stall interaction will vanish.
This result was also shown by Lehmann quite generally.
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APPENDIX C.
Part I
THRAOARTUM Flap =OAT WORK.,OF_N. N. BOGOLYUBOV
N., Ii.. Bogolyubov* is probably the most important Soviet contributor
uantum field theory at the present time. He has provided the first
gProus proof of the so-called "dispersion relations" for other than
liard scattering and this work has greatly stimulated the most promising
Plroach to quantum field theory at the present time.
In order to make a thorough appraisal of the work in quantum field
theory of Bogolyubov and his collaborators, all available translated
sources were read, including his published papers that are listed in
ppendix E. The past year has seen an exchange arrangement under which
reprints in quantum field theory and related topics are received from the
Laboratory of Theoretical Physics, Joint Institute for Nuclear Research,
DUbna, USSR, in exchange for publications on the same general topics
from comparable groups in the United States. Since Bogolyubov has
recently been appointed director of the Laboratory of Theoretical Physics,
this arrangement affords a good opportunity to2tollow his work. In
addition to the exchange arrangement and published translations of
Soviet articles, several other sources were used. Forcexample, the
page proofs of the first 428 pages of the forthcoming English version of
the. book Introduction to Quantum Field Theory by Bogolyubov and D. V. Shirkov
have been obtained recently. Unfortunately, the page proofs from the
entire book are not yet available, but those that have been received include
the first 34 of the 52 sections of the book. When Bogolyubov visited
the United States to attend the International Congress on Theoretical
Physics at Seattle, Washington, in September 1956, he presented, his
findings on dispersion relations, which were definitely the most important
presentation at this meeting. Because of the wide interest in his work,
he left it manuscript on The Problems of the Thoery of Dispersion Relations
(co-authors are Medvedev and Polivanov), which as subsequently
translated and circulated. A revised vernion of the manuscript has also
recently appeared in the Fortschritte der Physik. Bogolyubov later
sent in an important mathematical supplement to this paper tofl, the
Congress and it was then translated. In view of the special importance
of the paper, a careful study was made of the monograph of Bogolyubov
and collaborators, andalamof the mathematical supplement. Similar works
by other authors have been studied. Thus a good background has been
acquired to use in appraising the present work of Bogolyubov, even though
not all of his works have been translated.
*This spelling is used to be consistent with the system of trans-
literation followed throughout this report even though the translations
issued by the author spell the name Boboliubov and Bogolubov.
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As is characteristic of many of the world' best mathematical
physicists, Bogolydbov has made important contributions in several
different fields. He is funflPin.ttallY. a mathematician of great ability
whose contributions to physics have bee4,primarilythe presentation of
rigorous mathematical developmentsTOrConjeCtures or vague physical
programs that were proposed by others. The nearest parallel among
present Western Workers might be Professor F. J. Dyson of the Princeton
Institute fOr'Advanced-$tUdy.-He'altO began as A 1/101hfInatiCian and has
made 'contributions-that:are comparable'quartitativelyand qpnlitatiVely
to those of BogolydboV. Perhapt BogOlydbov't work is even more clearly'
:tathenaticai than that of'Dyson?.--An AIternatiyelgestern parallels,night-
be the late John von Neumann, although his contributions to mathenaties
are of a greater importance than those of BogolyUbov.
Bogolyubov first gained �wide recognition for his work with
N. Kryloff on nonlinear mechanics: A good summAry of the basic work
of Kryloff and Bogolyubov in this field is contained in the collection
of tapers translated by Solomon Lefschetz and published by the Princeton
University Press in 1943 under the title: Introduction to Non-Linear
Mechanics. his book gives a list of 40F references of the original
Soviet papers of the authors. As Dr. Lefschetz stresses, this Soviet
work introduced powerful new methods in nonlinear mechanics and gave
new importance to this field. It also stimulated general developments
in the theory of nonlinear differential equations.
Perhaps the text really outstanding contribution to Bogolydbarsmm
in the general theory of the statistical methancis of interacting
partitles. In this field he contributed particularly to the problem
of condensation of dense systems in approximate equilibrium. This '
field is too complex to review it here in great detail, but it should
be mentioned that. BogolyubOv did develop a hierarchy of differential
equations usually called the BBGKY equations because they resulted
from the work of the following people:- Bogolydbov, Born, Green, Mamma
and Yvon. This hierarchy of equations replaces the BoltzmAnn equation
of the more simplified presentations. Bogolyubov then showed a. neW
approach of approximation to the solution of this hierarchy of Emma
equations which depends primarily on classifying the various
characteristic time intervals in the relaxation of a dense syste4.,
Much work still remains to be� done in this field, but 'Bogolyubcres
papers constitute the starting point for many investigations.
Bogolytbov has made some contribdtions to problems of the t_
of the solid state. In 1950; be published, an important paper V14
polarOn problem, Whith deals with the effects of the polarliatio417
electrona within a crystal in suth'a way as to aead to a reductiOW��,,,�
the electron's energy and possible localization of the electron WOW
a uself-trappingu,nechanism. The first approaches to this problem
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ing a weak coupling expansion, i.e., an expansion in powers of the
detron charge. Difficulties In this method of expansion occur that are
lar to the difficulties of the perturbation theory of quantum �electro-
- ,cso, which have been discussed in this report. Bogolyubov developed
*strong coupling limit, which involves expansion in inverse powers of the
/effective coupling -66natant. 1/ The approximation of Bogolyubov is still
hadeqpate for an accurate treatment, and alternative approaches involving
termediate coupling have been developed by other workers (e.g., T. D. Lee
D. Pines). Much work remains to be done before a complete theory and
uantitstive agreement with experiment are obtained in this field, but
the work of Bogolyubov was certainly an important contribution.
An even more important contribution by Bogolyubov to solid-state
phIsics has been his recent contribution to the theory of superconductivity.
Present theories of superconductivity, stemming from the theory of
work rrohlidh, depend upon determining how the interactions between electrons
ection can, undPr proper conditions, create a, gap in energy between the lowest
rinceton state Of the system and the next highest state. Various workers have
inear devised theories that predict this energy gap and a specific model was
aal developed recently by Bardeen, Cooper, and Schrieffer. g/ The theoretical
yriet results of Bardeen and his co-workers had many attractive features but
gave artificiPally exclude many of the contributions that a general theory
=tents Would predict. Bogolyubov developed a much more exact Mathematical
fbrmdlation, which returned to the original Hamiltonian of Frohlich rather
choosing an arbitrary model, and he showed how to obtain more
)ov was rigorously an approximation that produced the same results as the theory
of Bardeen. 2/ The problem of superconductivity is still not fully
lem solved, but workers in this field generally agree that Bogolyubov's
recent Work has been a very important step.
ould
ial It is not surprising that Bogolyubov has made outstanding contributions
in Statistical mechanics and in the theory of superconductivity as well
Kirkwood, as in cipantUM field theory, for there are many similarities in the
ation mathematical treatment of these various fields of physics. In quantum
By field theory, the time dependence of relevant functions normally is
1KY given as exp L:iEt/h7where E is an energy. In statistical mechanical
problems, the probability function depends upon the temperature through
the function exp (--E/kT7. where T is the absolute temperature. Thus we
3 Bee that the time in the mathematical equations of vanttun field theory
correlates with an imaginary temperature in the equations of statistical
mechanics. This analogy is only one of the similarities between
!Ory statistical mechAnics and field theory. Another is that the creation of
the field, quanta can be made to correspond to a general excitation process
of in a statistical system. This mathematical similarity is in fact quite
in far-reaching and allows many statistical mechanical problems to be
rough computed by the method of FeynmAn diagrams, which was developed for
I Were quantum field theory and is the principal technique for practical
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quantum-ele,ctrodynamical,computations the-,present time. Thus,
of the ablest physicists. in, quantum field :theory (e.g., Ferman, ,Ge
�Brueckner, T. D., Lee; Yang, K. ,Watson) have recently made,
important contributions to,statistical problems, just as BogolYubot
don,e.
�
Functional Approach to quantum Field Theory-Renormalization Group,
� Quantum field theory was origins? ly developed by introducing non
interacting fields and then considering the _coupling between these
as a perturbation. This method of presentation has the advantage
the dependence of the original Lagrangian of the system on the field
operators is usually ,given in a relatively simple form. However, theee
fields -which correspond to ,"bare" particles -without interactions do
describe the real physical, ,for even a real isolated partic
interacts with the quantumi fluctuations of the other fields in the
va,cuum., Thus, the renormalization problem had to be introduced sq as.
to obtain the quantities correeponding, to real vantities from those
originally introduced in, the theory.. Because of the infinities invol
in, relating the real.particlea to "bare" particles, a new approach has,
been developed in recent: years which attempts to define the basic the
entirely in terms of the quantities for real particles.� Thus, it is
assunied that the fields are, already renormalized. In this case, one
does not know ex-plicity_how the. .field operators enter into the Lagr
or ot,her imports.nt quantities, �such as the scattering matrix S. Never-
theless certain general mathematical relationships between these
qnsntities can be determined. �-Bogolyubov. has been one of the many people
who have �contributed. to the de:velopment of these general mathematical
formulations. One assumes that a quantity such as the scattering matril
is a general functional of the fields 4P(x) and introduces the concept
, of p. functional. derivativeriar(x). This fun.ctional d.erivative is a usd-
fta_generalization of the idea of an ordinary derivative and it expresses
the way in which S -varies when the operator suffers a � small alteration
in the neighborhood of x. (This statement is nonrigorous but gives the
general idea,) BogolyulDov published a paper 1954 that contributed
to the .development of this formu.lation, and. he and. Shirkov have used it
extensively, in their work on tha qpnntum theory of fields. Many quantities
can be expressed very succinctly, in terms of theae functional derivatives,
and Bogolyubov has used them to define the generalized currents of the
theory and. to reformulate the causality principle. In his work on the
functinnal approach to quantum ,field. theory, Bogolyubov was to a large
extent simply stating the research results of other people in slightly
different form. �
Bogolyubov and, Shirkov have also introduced the idea of a "charge
renormallization, group" in quantum field theory. This is a Lie group of
transforn?ations that can be introduced to clarify some of the ideas of
the renormalization process and. to remove same ambiguities in it. The
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technique has permitted the authors 'to' some of the steps in
pertUrbation-procedures And in particUlAr to deal with some of the
probleks connectecLvith-the introduction of ap-artificial cut-off of
large momenta. � It is not felt that the work mentioned was of unusual
importancel-but it was certainly sound work that 'helped improve the
fortaliam of vAntum field theory and constituted the first appreciable
contributiona.of'Bogolyubov-inluantum field. theory.
. Indefinite Metric
One of the major problems in quantum field theory is the intro-
duction of infinities by the renormalization procedure. At first,
workers in this field thought that these difficulties should be
associated with the use of a perturbation procedure, but it was later
proved by various theorists (principally Kellen of Sweden) that
infinities must occur even if the theory is treated accurately with-
out the use of the perturbation method. Kellen and Lehmann showed
that the divergencies were a very essential property of the theory
related to the singularities of the Green's functions.
In the case of the renormalized coupling constant, these functions'
are 'defined over all space-time, but become infinite on the light cone.
'It was hoped at first that these infinities in the Green's function
Mmight be removed, or at least decreased, by.the-normalization procedure.
talon. and ;LehMann provedilv very general argumental that the
renormalized Green's functions must at least be as singPlar as the
Original functions. This result shoved that it would be difficult
to-prove the logical consistency of quantum field theory. Furthermore,
:'t' seemed to"'prevent-the construction of nonlinear theories of a
tisfactorytind.
The Lehmann-Kallen theorem depended upon some very general
mathematical postulates; one of these vas that the appropriate space
which to describe the states of the quantum field is a "Hilbert
pace.' This is a generalization of a vector space to an infinite
4mber of dimensions. All of the states in this space have a positive
rm, i.e., all vectors have positive length. Heisenberg and _othPrs
Ilagested that the difficulties posed by the Iebrinnn-Kallen theorem
be avoided by introducing states of negative norm. These would
resPcnd to States with a "negative probability." Such a space, in
ich the length of vectors can be either positive or negative, is
to have an "indefinite metric." These negative probabilities
NtouclY have no direct physical meaning. Earlier, Gupta and
1641er had used a theory with such an indefinite metric to carry
the quantization of the electromagnetic field in such a way as..;
P"PerlY eliminate the longitudinR1 photons, and they had shown
�tlie indefinite metric does not need to lead to unphysical results
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if the real physical states are limited to the,subspace of the states
of positive norm. , Bogolyubov and Shirkov considered in quite general
fashion the usefulness of introducing such an indefinite metric. They
find that there are difficulties with the use of indefinite metric and
that its introduction does not appear to offer a.lartiollarly simple
solution to the problems of nonlinear quantum field. theories. Interest
in the idefinite metric in quantum�field theory stems now, in great Part
from use of such a metric in the program of Heisenberg for a unified
field theory for elementary particles. This program is still too indefi
to permit any clear appraisal. The publications by Bogolyubov and Shirkav
as well as articles by thdir associates on the sUbject of the indefinite
metric, such as a 1958 preprint by Medvedev and Polivanov entitled
On a Classical Model of Indefinite Metric, indicate that Soviet workers
are -continuing their interest in this field.
Causality and- Dispersion Relations
The .work of Bogolyubov and collaborators on the rigorous derivation
of dispersion relations in quantum field theory is believed to be the
most important contribution that Bogolyubov has made in quantum field
theory.
The work on the prof bf the dispersion relations by Bogolyubov
and his co-workers represented an outstanding piece of work which was
extremely difficult from a technical standpoint. The most difficult
part was the mathematical supplement, which appears to have been done
by Bogolyubov alone. The methods that be used have since been
simplified by Bremermann, Oehme and Taylor, who have restated his
proof in terms of- general theorems about the holomorphic envelopes
of domains of many complex variables. However, some idea of the difficulty
of BogolyUbov's theorem can be gained from the fact that it took these
three expert' 'workers over 6 months to restate Bogolyubov's proof; they
agreed that it,was-.very unlikely that they wculd have come to a proof
of the -theorem without Bogolyubov's theorem to guide them.
The essential step in these proofs, as has been clarified by
Bremermant, Oehms.and Taylor, is to extend functions which are originally
proved to be analytic in a small domain, called D. Then by very general
theorems it is proved that any function which is analytic in a domain
D must also be analytic in a larger domain DI which is the pseudo-convex
hull of D and is called the holomorphic envelope of D. While the domain
D is by itself not large enough to prove the dispersion relations the
extended domain is.
The proof of. Bogolyubov and,.his,group,stimulated.many.other workers.
The current proofs-for::dispersion relations, are found to. be valid only -
for those valUes:Of A� less- thana-certain..maximum-value of Llii-eiEs
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As the proofs have been improved, the value of A numc has been increased.
This is done as better and better methods are found for approximating the
holomorphic envelope. The Soviet workers beat value for Alii2 max was
approximately 2 /,1, where tt is the pion rest mass. More recently an
explicit representation has been found frOmtthe work of Dyson, Jost, and
Lehmann, whiehA21 ows one to extend the limit' for .4662T max to about 314
These last, three workers have shown that he current methods of proof
cannot be extended to greater value of 41 4 max because they have a counter
example for which dispersion relations break down at this critical
momentum transfer. This example is not sufficient to prove that the
dispersion relation is not really valid for a great momentum transfer,
for the current proofs do not bake use of the unitary principle, which
may easily extend the range of validity of the theorem-
Dispersion relations have now been proved for other Processes in
addition to pion-nucleon scattering. The methods of Bogolyubov, as
extended to date by others, have not been sufficient to prove dispersion
relations in many interesting cases. For example, dispersion relation
for nonforward scattering of nucleons by nucleons cannot be proved
rigorously. It is clear that the Soviets appreciate the great importance
of Bogolyubov's achievement in this proof because it was cited as one of
the major reasons that he was recently awarded the Lenin Prize.
,Possible Future Work of Bogolyubov
Both in the USSR and in other countries, many applications of
dispersion relations have been made. The Soviet workers have also
applied dispersion relations to photo-prodaction and scatteri ng of ix1.6ns
by deuterons. The Soviets seem to be aware of the full potential of
�dispersion relations. They have begun considering relations in which
�A. is varied and CO held fixed, which has recently shown promise of useful
applications. All or nearly 8.13 the important work in the USSR on
dispersion relations in qpnntum field theory is probably coming from the
laboratory of Theoretical Physics of the Joint Institute for Nuclear
Research, Dubna, USSR; Bogolyubov is now ai rector of this Laboratory and
'this work is presumably a result of his influence and interest in this
Veld. Some idea of the amount of effort in this particular field in
USSR relative to the rest of thel world may be indicated by the
allowing comparison. A bibliography of all significant papers related
the development of dispersion relations in quantum field theory was
04ad. to contain a total of 187 papers of which 37 are by Soviets. 4/
above comparison may be somewhat misleading because it is obviously
ier to obtain papers of Western workers.
� It is difficult to predict exactly what the future contributions
the Soviets will be in quantum field theory. The usefulness of the
sPersion relations as such will probably decrease and emphasis will
bably shift to other generalcconsequences of the analytic properties
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ofrthe..Scatterin�unCtions. , Of,:course,,this.is:a,closelyrelated
f4.1c1,,,.Recent_major,aChievements 14(this'directipn have been the proof,
of the "CF] theorem". in,thisJlay,by.the,Smisaphyaicipt-Jost ancla
general proof of the connection.-between spin and statistics .by }1.4rgoyne,
and,by.Luders and:-Zumino TWPoWets,have not as yt.made. an outstandi
contribution in-this particular:direction,but there,seems-tobe every-
reasonto-expect.tbat they,Will'Ao:So* IheSoviets are quite competent
In the basic field of mathematics., yhich40 most_cIosely-related to thjs.
particular field of:pilysicavt4iStbe:t4POry.Pf functions of .several
complex variables.,
;c4.. longer raw 1;;aal,a, it is clear that new ideas are needed in .
quantum 'field theory and that a further development is very:-apt to:
require a combination of the methods already developed by BogolydbovI.Ahe
theory of functi,onspf several complexyariables, and.a much-more detailed,
understanding of Such nonlinear.:relationships.as the unitary principle.:
It appears that-BogOlylabov.will be as apt to make a fundamental contribut
to this4mport8.nt:field of mathematics as any other single worker iii this
field.
_ A23
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Let g
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Using
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Furth(
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� 20,1Z-8141-1-0-1*L�TYSrl3NEr
PART II
BOGOLYUBOV'S DERIVATION OF DISPERSION RELATIONS
� The term '.'the assumption of causality", as used in current work in
quantum field theory, refers to the physical assumption that "no effect
can be observed before its cause." While this may seem to be a very
obvious and trivial requirement, it actually places severe limitations
on the mathematical properties of a theory that describes �a linear
scattering system. The nature of this mathematical correction and the
need for it will be explained briefly. Assume that an input or source
is introduced at the time tz--0 and then removed almost irTmPdiately.
Let G(t) be a function that gives a tiniel dependence of any resulting
physical observable. This will be called an output scattered wave.
The input at t7----0 can excite many transients in the physical 'system
and therefore an output G(t) may- continue to be observed for a long
time after the input pulse has stopped. However, the output cannot
occur before the input, and therefore G(t) must equal 0 for t < 0.
Let g (6,1) be the Fourier transform of the output G(t), which is
given by
g (03) 1G-to e
t t
-00
Since G(-t) vanishes for t... and I 2 > are any possible states of the system. metric
is used in. which the space-time length is positive for time like
directions and negative for special directions..
The causality assumption alone is not enough for the derivation of
dispersion relations in quantum field theory. In addition, we must use
the f'ollowing general limitations on our theory:
(1) Relativistic Invariance: The relativistic invariance of the
theory demonstrates that the cormnutator expression written above must
be Lorentz-invariant so that e.g., if I 1> and. I 2>are both the
vacuum state 0> , this expectation value is a function of only
the one 4 -ve ctor (x-x') and not a function of both x and xl separately.
Furtlaerznore, such expressions can depend upon the four components of
x-xt only through the Lorentz-invariants of these quantities when
combined with the other vectors, tensors, etc., in the theory. Thus,
the principle of relativistic invariance leads to a very large, reduction
in the number of variables of the theory and. simplifies the form of
many f'unctions.
(2) Asymptotic Condition: It is assumed that each of the local
field operators for the interacting system approaches (in a proper
mathematical sense) a solution of the equations for a noninteracting
system when the differences and, times involved become infinite.
. -Energy-Spectrum:.-A natural assumption is made that a vacuum
is the state' of lowest energy-sa:,that all other states have positive -.
energy. Each operator of the theory then basa:spectral representation:
.'terms of the contributions from the states of different!:energyAn the
V*oi.y. These states include both discrete or bound states and
continuum states.
One other very strong restriction that: a true 'quantum field should
satisfy is the unitary principle. This principle eipresses the conservation
or probability and is .given mathematically by the requirement that the
3-.pmatrix must be unitary. This particulAr requirement has not been used
' in most of the proofs of dispersion relations that are discussed
6 -
ROR-AR-10-111L�TISE-01TLY
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-.PQR-QFK-e-Itr-TriTEr
Since the 1954 paper of Gel1LMann, Goldberger and Thirring, maw
workers have developed dispersion relations.jm,quantum field. theorr.
However, the original presentations, lacked much rigor and the relati
should properly have been considered. as conjectures-, although it was
generally expected that they follow from very general,principles.
relations were extremely valuable in theoretical physics; e.g., they:,
allowed Anderson and his group to determine the Fermi-Yang ambiguity'
in the.phase shifts for the scattering of pions. Furthermore, the
dispersion ,relation for forward scattering alloyed a general determin
of the coupling constant between pions and nucleons. This was the firl.
time that this basic coupling constant, which characterizes the stre
of nuclear forces, could be determined in a manner free from the great
difficaties.of perturbation theory or other types of approximations.
Many applications were made of, the dispersion relations and they were.
found to be in good agreement with a wide variety of experimental resul
However, there were many difficulties in proving the dispersion relation
for particles with finite mass and for scattering in directions other_
than,the exactly forward direction. The first rigorous proof Of -
dispersion relations .for the forward direction ini field theory was givom
by the German physicist Symanzik. Only slightly later and independently
BogbIyubov-and his- cowbrkers developed a, woof of a dispersion relation:
for pion-nucleon scattering that was valid for all directions of scatter-
ing. The relation, which was conjectured earlier by Goldberger and other
involved relating scattering amplitudes for various energies GO, but
,all for the same value of the momentum transfer .
This proof of dispersion relations vas first shown to Western worker
by BogolyUbov in Seattle and was then circulated in a paper entitled:
The Problems of the Theory of Dispersion Relations by Bogolyubov, Nedvedef
and Polivanov. While this proof is necessarily very intricate, it involve
the following important parts: ,
(1.) The use of a particular representation for the scattering
amplitude of pions of energy A (6) ) scattering of pions through
momentum transfer . This representation Utilizes the spectral
properties,of-vacuum operators in accordance with earlier investigation
of Lehmann,and others.
(2,) The expression for A (co ) depends upon the rest mass M.'
When N2 is positive, it is not possible to give, an easy proof of dispersion
relationt,,HbweVerl. the relations are easily proved if, the parameter M2 is
.'chosen less than�(-462).,...:The proafAs,therefore carried' out first. for
suchmegative.values-of the M12:and.the'necessary analytic properties of
A( 6) i11-) "are proved dn'this case.,:lhen an analytic continuation' in the
rest mass iS:made back to,the.physically'meaningfUl real 'positive value.
ZO�Fr-OFF-10-Tritb-IISE-CMGY�
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r',Y.
ationi-
was
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hey
ity
Le
almtnation
le first
3trength
great
ions.
were,
1 results.?
tblations
other
ras given
,endently
?elation:
r scat"
and otbeX
A.) int
emn. wer
itled:
iv, Med% /
, it iur
cering
3 thrall
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t MASS
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Approved for Release: 2022/03/16 C06927295
NM OFFICIAL um-amr-
In order to prove that this analytic extension is possible, use was
made of a powerful theorem dealing with the analyticity domain of a
certain generalized function of five complex variables and one real
variable. The proof of the necessary properties of this function is
provided in a mathematical supplement by Bogoiyubov.
- A28 -
FOR OFFICIAL U$! CALI
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OFFECIIkt-USElanr
APPENDIX D
BASIC DATA LIST .
� The following list was extracted from the bibliography of appendix C,
part II. It constitutes the basic dateClromWhieh the tables in the' -
discussion were drawn and upon Which:moat of are based.
The list gives the Various authors, their institution, and the number.
of articles which they published, eithet altos, Or jantly. The-folibwingi'
data on Bogolyubov have been excerpted to use as an example in explaining
the system:
1953 1954 1955 1956 1957';1958
Bogolyubov, N. N. Leningrad State Univ. 1!
2
2 8/2 5/2 2/34
(1) Numbers appearing in any given column repreSent articIes'brig:inally
*blished in that year (usually in Russian), although abstracts and/or
00eviews appeared at a later time.
(2) Numbers appearing to the left of the dotted Vertical line wider
the 1953 column refer to articles found abstradted, etc., in 1953, but
sriginally published before 1953.
(3) Whole numbers, or integers, refer to papers rpublished by the
alone.
(4) Fractions refer to joint anthorships.
The denominator indicates how many authors wrote the article
ncluding the author opposite whose name the number appears).
The numerator indicates to how many distinct articles of� that
et of authors the particular author contributed. -
-TUE the 1 in the 1953 column oppOdite BogoiyubeV's name.indicateaL
tte published one paper alone in 1953.. /n-1954, he published two
One' and collaborated with another author on one article. In 1958, he
43,00rated with three authors on two separate articles; and he
berated With four other authors in One more article.
- A29 -
-VOR-OFFESE-OrdEr
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Abrikosov, A. A.
Aleicseyev
Aleksin, V. F.
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jzoL.Qmest_L-lz_,E7orr
1953 1954 1955 1956 1957 345
Inst of Physical
Problems
Vavilov, Acad. of
Sciences, USSR
Physics -1;nst line)*
,P; Lebedev,!Ace4
of Sciences, USSR
:
Physics Inst imena.
P. N.:. Lebedev,.. Acad
Sciences, USSR
Ukrainian Physico- 2/2
lust, AS,
Ukrainian SSR
Mos cgy-:Englaaeering
� P21ys1,05: Inst � . -
Ukrainian Physieo-
Te ohmic:al Inst AS)
Ukrainian &SR
Arzlaanykh, I. S. Dist of Math and
Webanies imqni.
V. I. Roinaanovskly,
AS, Uzbek SSR
Electrophysical
Labs, -AS, US...
Askaryan, G. A. Physics Inst imeni
.
lebedev,, AS,
USSR
Asanov, A. R.
Averbakh,.
:Physics past 4meni
P.. N. iiebedev, AS,
USSR .
Avrorin, Ye. Physics Inst imeni
P. N. Lebedev, AS,
USSR
-A30 -
JEQS-SMEICIPA-1313*-02TLY
5/3 2 2/3
1
2
1/3 3.
go-heia
Biaan,
V
Bakarov,
Beleai31
(decease
Beiyal
%rest&
Bilenki:
Blathin
Bogolyu
�Bonch-I
V. L.
Borgare
Bbrovi.
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198
Baldin, A. M.
Bayer, V. N.
Bazarov, I. P.
Approved for Release: 2022/03/16 C06927295
_ECEL-Oggxcva,--tmE,en-r-
� . Chief Administrator,
Main Administration
for Utilization of
Atomic Energy
Physics Inst imeni
P. W. Lebedov, AS USSR
Belenkiy, S. Z.
(deceased 1956)
Belyayey, S. T.
Etrestetskiy, V.
gdlenkiy S. M.
Tank,
.sachintsev,
V. Z.
Inst of Physics, AS,
Ukrainian ssg
Moscow State Univ
1953 1954 1955 1956 1957 1958
1 2 3 2i
Physics Inst imeni
P. N. Lebedev, AS, USSR
Inst Atomic Energy,
AS, USSR
B. Physics Inst imeni
P. N. Iebedev, AS, USSR
Joint Inst fOr'
Nuclear Research .
Moscow State Univ
D. I. Joint Last for
Nuclear Research
Iimplyuloov, N. N.
th-Bruyevich,
t A. A.
evikov, V. A.
Leningrad State
Univ imeni A. A.
Zhdanov
Moscow State Univ
Dnepropetrovsk '
State Univ imeni
300th Annitrof
Union of Russia.
and Ukraine
- A31 -
1
1
1 1
2 2
11/3
- 2 1
11 * �24 2 8/2 5/2 2/3/i
_E011-01*-1-e-IA-L�Wirl3NEr
.
proved for Release: 2022/03/16 C06927295
3.
1/3
4 1
1
11
Brodskiy, A. M.
Budker, G. I.
pproved for
Release: 2022/03/16 C06927295
1953 1954 1955 1956 155
Moscow State UmitYbktlif1/3 cy...-.F.1:2/3 2
Inst Of Nuclear 1
Physics Siberian
Dept, AS, U$SR .
Buymistrov, V. M. .Inst of Physics, AS,
Ukrainian SSR_
Bychkov, Yu. A.
Acad. of Sciences
USSR
ChavchanidzelrV. V. Inst of Physics,
Acad. Sciences37
Georgian SSR
Chernayskiy, D. S. MOSCOW Mining
Chang-Lee
Chou�lCuang-Chaq
Chernayskiy, D.
Cytovic V. ,
Demkov, Yu. N.
Dolginov, A. Z.
Duan-I-Shi
S.
Inst imeni I. V.
,=Stalin
Leningrad State
Univ imeni A. A.
Zhdanov
Joint Inst for
Nuclear Res (Lab
.:of Tbeor Phys)
Physics Inst imeni
F. N.4Lebelev, AS,
USSR
Moscow State Univ
Leningrad State 1
Univ inieni A. A.
'..Zhdanov
Leningrad State
Univ imeni A. A.
Pidanov
Joint Inst for
Nuclear Research
A
- A32 --
-_FLou�diapgie---#A-15Thi+
?0,3
1
1
:
ter,
erg
400noy
Aka'
(kalasin,
GdylDraSa
. Gel 'land
'GI= burg
Ginzburg
1111111111111111.IIIIIIIIII"MilrAT�DDroved for Release: 2022/03/16 C06927295
7 1958
1
Approved for Release: 2022/03/16 C06927295
Dyatlov, I. T.
Dykman, I. M.
Faddeyev, L. D.
Faynberg, V.Ta.
ftdorov,
leYnberg, Ye. L.
imonov, G. F.
dkia, Ye. S.
Ya. I.
A. D.
B. T.
1953- 1954* 1955, 1956 1957. 1958
. Leningrad Physico.-.
Technical mat, AS,
USSR
Inst of Physics AS,
Ukrainian SSE
Ieningrad State Univ
,imeni Ao.VA,Ahdanow
Physics Inst imeni
P. N. Lebedev, AS,
USSR
Inst of Physics and
Math, AS, Belorussian
SSR
1/3
1
Physics lust imeni
1
2
P. N. Lebedev, AS,
USSR
Moscow State Univ
1 �
7
Physics Inst imeni
12/2
21-
P. N. Lebedev, AS,
USSR
Deceased 1952
1 :
Inst Physical
3.
1/3
Problems imeni
S. I. Vavilov,
AS, USSR
Moscow Pedagogical
5
Inst imeni V.I.
Lenin
Moscow State Maly
1/3
MoscoW State Univ
3.
Physics Inst imeni
1.
P. N. Lebedev, AS,
USSR
- A33 -
�E0ELCORSZCAAS-I3Se-OHLT-
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Goltfand, Yu. A.
Goluberikov, V. N.
Gortkov, L. P.
Grigoryev, V. I.'
Gurevich, A. V.
Gurzhi, R. N.
pproved for Release: 2022/03/16 C06927295
-20R-41W0-17ktrflOrtnr
1953 1954 1955 1956 1957 192
Physics Inst imeni
P. N. Lebedev, AS4
USSR
Inst of Physical
Problems imeniva#I.:.�.�:
Vavilov, AS, usw
Moscow Petroleum
Inst imeni I. M.,
Gubkin
Moscow State Uniy.�
Physics Inst imeni
P. N. Lebedev, AS,
USSR
Ring En Joint Inst for
Nuclear Research
Heber, Va. G. Joint Inst for
Nuclear Research
Ingarden, R. S. Physics Inst,
Polish Acad. of
Sciences .
Ioffe, B. L.
Ivanenko, D. D.
Izmirilov, S. V.
Kalitsin, N. E.
Ullman, V. I.
Kaschluhn, F.
1 1?
1 ,
2 .
li 12/2 2
1
Acad of Sciences, 2 1/3 1/3 1 1/3
USSR
Moscow State Univ
State Univ Of
Bulgaria
Minsk Pedagogical
Inst imeni
A. M. Gorkiy
Joint Inst for
Nuclear Research
- A3 4 '
1:1
2/ 3
1
1
1
Kerimay.
Xhalatn:
lbalfin
Ktasbni
lhokhlc
Khrist4
Kirzhn
Klepik
Klimor
KObozc
Koles3
Kompa
Korst
Krokk
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1
1/3
2
St, N.
*bin, 0. N.
Approved for Release: 2022/03/16 C06927295
'141' !!"--
Kerimov, B. K. Moscow State Univ
Ihalatnikov, I. N. Inst of Physical
Problems imeni
S. I. Vavilov, AS,
USSR
Khalfin, L. A.
Khlebnikov, A. K.
Khokhlov, Yu, K.
Khristov, Kh. Ya.
Kirzhnits, D. A.
nepikov, N. Pc
montovich Yu.L.
Kobozev, N. I.
lesnikov, N. N.
All-Union Inst of .
.Prospecting Physics
Acad.of Scieneee;
USSR
Physics Inst imeni
P. N. Lebedev, AS,
USSR
Moscow State Unix
Physics Inst imehi
P. N. Iebedev, AS,
USSR
Lab of Nuclear
Problems, Joint
Inst for Nuclear
Research
Moscow State Univ
Moscow State Univ
Moscow Power
Engineering Last
imeni G. M.
Krzhizhanovskiy
eyets A. S. Inst of Chem Physics,
AS, USSR
Moscow State Univ
Acad of Sciences,''
USSR
� � ' �
'
1953 1954- 1955 1956 1957 1958
2/2
'4/3- 1 3/2 1i
1/32/3
2�
__IUA-Gn4e-ML-trJr-ONLY-
1
pproved for Release: 2022/03/16 C06927295
1
1/3
1
1/3
2 1
1/3
2
J.r
Krolkowskiy W.
KUdryavtsev, V.
Knni, F. M.
Kurdgelaidze,
D. F.
Kurtenkov, L. A.
Landau, L. D.
Lapidus, L. I.
Lebedev, V. I.
Lipmanov, E. M.
Livsbits, M. S.
Logunov, A. A.
Lomsadze, Yu.
7-
Approved for Release: 2022/03/16 C06927295
8.
153 1 5It19
Inst of Physics1.1
Polish Mad of
Sciences
Leningrad State
Univ imeni A. A.,
Wanov.
Latvian State Univ
Moscow State Univ
Inst of Physical-
Problems, imeni
S. I. Vavilov, A.
USSR
Lab of Nuclear
Problempoint
Inst foi 'Nuclear
Research
Moscow State Univ
Novozybkoi.
Pedagogical and ,--
Teachers Inst
Inst of Physical
Problems imeni
S. I. Vavilov, AS,
USSR
Moscow State Univ
Science Res Inst
of Physics, MoscoW5.
State Univ
-A36-
1/3
2:2
A ��,-,,,pri for Release: 2022/03/16 C06927295-
Approved for Release: 2022/03/16 C06927295
1956
-
1958 1953 1954 1955 1956 1957 1958
1,3
Maksimenko, V. M. Physics lust imeni
P. V. Lebedev, AS,
USSR
Mhrkov, M. Physics Last imeni 1 1 2
P. N. Lebedev, AS,
USSR
Matveyev, A. N. Moscow State Univ 1 1 1/3 1
Mayer, M. E.
Medvedev, B. V.
Mickevic, N. V.
(Niskevich)
Migdal A. B.
Mikhaylov, V.
:Joint Inst for
Nuclear Research
Math. Inst imeni
V. A. Steklov, AS,
USSR
Moscow State Univ
Acad. of Sciences,,,
USSR
Physics Inst imeni
P. N. Lebedev, AS,
USSR
1
2
Minlos, R. A.
Mirianashvili, N. M.Mbscow State Univ 1;
Natanzon, N. S.
Reganov, B. S. Joint Inst for
Nuclear Research
� . . .
Nelipa, N. F. Physics Inst,imeni 1;
Lebedev, AS,
USSR
'Ncvozhilovl Yu. V. Leningrad State
Univ imeni A. A.
Zhdanov
-A37..
itzLatzczAL-�uenr-
pproved for Release: 2022/03/16 C06927295
1
2
2
2
1
2
1 1
1
1
2
1
2
Ogiyevetskiy, V. I.
Okun, L. B.
Ovsyannikov L.
Parasyuk, 0. S.
Pekar, S. I.
Peterson, V. R.
Petras, M.
Podgoretskiy
(M. I.)
Pokrovskiy, V. L.
Poliyevktov-
Rikoladze, W. M.
Polivanov, N. K.
Poloviia, R. V.
Pomeranchuk, I. Ya.
Pontecorvo, B.
(M.)-
Popovici, A.
p�roved for Release: 2022/03/16 C06927295
1953 1954 1955 1956 1951
Electro Physical^' '
Lab. - Now parbo
Joint Inst for
Nuclear Research
Joint Inst for4''4 '�
Nuclear Research
Inst Mathematics,o
AS, Ukrainian Sag
--
Inst of Physics,.
AS, Ukrainian SSR'
Physics Inst emini
P. N. Lebedev, AS
USSR
Yeniseysk Teachers
Inst
Moscow State Univ
Leningrad Physico
Technical mat, AS
USSR �
Joint Inst for
Nuclear Research
(Formerly an
Italian citizen;
bow a Soviet)
Aa8
-44111'16F-161-7177715177
1
11.11111111111111.1.1111111.1111.1.1.11.1mmAporoved for Release: 2022/03/16 C06927295
g
1
3.
2
ovy
ROSik,]
Brizanov
Ryndinp
RZeVusk:
Sannika
Shirkov
Seldowi
(See Ze
Mi. B.)
2/2
2
Approved for Release: 2022/03/16 C06927295
Pugachev, Ya. I.
Rayski G.
Ryazanov, M. I.
Ritus, V. I.
Rosental, I. L.
ftdik, A. (P.)
Hume Yu. B.
Muusik, I. Kn.
1953
1951i 1954
1955
1956
1957 1958
1
2
� Inst of Theor Phys
1
(Poland) Copernicus
Univ
Moscow Engineering-
1
Phys Inst
Physics Inst imeni
1
2
P. N. Lebedev, AS
USSR
Physics Inst imeni
1
2
1
P. N. Lebedev, AS,
USSR
Inst Physical
1:
2*
� 1/3
Problems imeni S. I.
Vavilov, AS, USSR
Yeniseysk Teachers
3:2
Inst
Inst of Physics 1
and Astronomy,
,Acad. of Sciences,
Estonian SSR
anov, G. V. Moscow State Univ
emyski, j.
V D. G.
kPv, D. V.
tsch, J. B.
elidovich
20 '
1
Lab of Nuclear
1
2
.Problems, Joint
Inst for Nuclear
Research
Polish physicist
2
1
1
2
Moscow State Univ
1
2
-A39-
-Eal3j)*WEAirlf5E617L7
pproved for Release: 2022/03/16 C06927295
Shapiro, I. S.
Shirkov, D. K.
Shirokov, M. F.
Shirokov, Yu. M.
Silin, V. D.
Sirkov, D. V.
p�roved for Release: 2022/03/16 C06927295
Moscow State Univ
Moscow Aviation
Inst imeni S.
Ordzhonikidze
1953 1954 1955 1956 1957 i
2 � 1
. '5/2 4/2 .2/2
"
tatorn
fezY)
Moscow State Univ 2 1 i 31 Slidzim
Physics Inst imeni 1i1/3 Illassar,
P. N. Lebedev, AS,
USSR ThrYan
Skobelkin, V. I. Moscow State Univ
Smorodinskiy, Ya. A. Lab of Nuclear.
Problems, Joint
Inst for Nuclear
Research
Sokolik, G. A.
Sckolov, A. A.
Sbkolov, S. N.
Sokolov, L. D.
Solovyev, L. D.
Solovyev, V. G.
Solovyev, A. N.
Stepanov, B. M.
Moscow State Univ 1
Moscow State Univ .213/2 11.7 2 3/2 1 2/2 1 1/3;
1/3. .V3
Joint Inst for
Nuclear Research
Lab of Nuclear
Problems, joint
Inst for Nuclear
Research
Lab of Nuclear
Problems joint
Inst for Nuclear
research
Moscow State Univ
Moscow State Univ
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1 1
1 1
2
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1/3
410, I
arasoN
Temko,
Tatre
Terlet1
Ter-Ma
K. A.
Ternov
Teviky
Tsytol
Tula,
1958
/2 1 13=
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Stratonvich, R. L.
Sudakov, V. V.
Suffezypski, M.
Svidzinskiy, A. V.
Taksar, I. M.
Taltyanskiy, I. I.
Tamm, I. Ye.
Taxasov, Yu. A.
Temko, S. V.
Tavkelidze, A. N.
F__a4--QUIC7TAT:r4/S:E"algrir-
1953 1954 1955 1956 1957 1958
L' vov State Univ
imeni I. Franko
1
Leningrad Physico-
3 2/2
Technical Inst
1/3
Polish, physicist
Moscow State Univ
3.
Latvian State Univ
1
2
Livov State Univ
imeni I. Frando
1
Physics Inst imeni
1:
�
1/3
P. N. Lebedev, AS,
1/3
USSR
Moscow State Univ
Joint Inst Nuclear
Research, Moscow
State Univ
Ttrletskiy, Ya. P. Science Research
Bast of Physics,
Moscow State Univ
Ter-Martirosyan, Physico-Technical_
A. Leningrad Inst,
AS, USSR
Ternov, I. M.
,Tvikyan, R. V.
Moscow State Univ
Yerevan State
Univ imeni V. M.
Molotov
eytovich V.N. Moscow State Univ
Tula A. V.
Leningrad State
Univ imeni A. A.
Zhdanov
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Tumanov, K. A.
Tyablikov, S.
Ulegla, I.
Verle, I. I.
Volkov, D.
Votruba, V.
Vyalov, G. N.
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_raL-or4-141ortitzt-onr." -
1953 1954 1955 1956 1957 1958.
2
Moscow State Univ ZhArkov,
Math. Inst imeni 3i2
V. A. Steklov, , .z�
Zyryanol
AS, USSR
Joint Inst for
Nuclear Research
Joint Inst for
Nuclear Research
(Polish physicist)
Physics Inst imeni
P. B. Lebedev, AS,
USSR
Yaglom, A. M. Inst Geophysics,
AS, USSR
Ynichnitsyn, V. G. Dnepropetrovsk
State Univ imeni'
300th Anniv of
the Union of Russia,
and the Ukraine
Yappa, Yu. A. Leningrad State Univ
imeni A. A. Zhdanov
Yeleonskiy, V. M. Ural Polytech Inst
imeni S. M. Kirov
Zaytsev, G. A. Ivanovo Chemico-
Technology Inst
Zariavenko, L. G. Joint Inst for
Nuclear Research
Zel'dovich Ya. B. lust of Chemical
(Same as Physics, AS, USSR
Seldovitsch, J. B.)
-A42.
1:
22uarraglartyst-tyfiry--
1
1
1
1
4
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1958
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Zharkov, G. F.
Zyryanov, P. S.
Physics Inst imeni
P. N. Lebedev, AS,
USSR
Ural Polytechnical
Inst imeni S. 14.
Kirov
1953 1954 1955 1956 1957 1958
1 1
jaLagracZA33-um-anty-
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gmpix E
BIBLIOGRAPHY
This bibliography isa complete.listing ofaII the. articles of
interest in this. study. It was compiled by canvassing all the
appropriate available journals* on quantum field theory. Where an
article bas,been abstraotedor reviewed, those references are also shown.
About 25 of the articles listed in the bibliography are preprints
from the Joint Institute for Nuclear 'Research in Moscow., These articles
are designated by the word "Preprint" in parentheses at the end of the
citation.
Abrikosov, A.A.
IrOn the Compton Effect and Mutual Scattering of Particles at High
Energy in Quantum Electrodynamics and Fteudoscalar Theory,"
DAN 102, 1097** NSA 6551 (1955)
"On the Infrared Catastrophe in Quantum Electrodynamics," ZhETF
96 (1956). MR 18, 174 (1957)- Phys Abs 4811 (1956)
"Scattering of High Energy Electrons by Electrons and Positrons,"
ZhETF 303 (1956). Phys Abs 6704 (1956)
and Khalatnikov, I.M.
"Asymptotic Ekpression for Green's Function of Electrons in Quantum
Electrodyirmics," 77311954). NSA 4469(J954)
"The Use of Two Limiting Momenta in Field Theories," DAN l3,993 (1955)
MR 17, 565 (19564
and Galanin, A.D. and Khalatnikov, I.M.
"Green's Functions in the Theory of Mesons with a Weak Pseudoscalar
Coupling," DAN a, 793 (1954). MR 16, 317 (1955)
NSA 7145 (1954)
Phys Abs 7970 (1956)
----- Galanin A.D.; Joffe, B.L.; and Pomerancuk, I.Ya.
"Green's Functions in Meson Theories," Buoy.� Cim VIII, 782 (1958)
AkbbreViationA-fOr the journals are fond at the end Of the bibliography.
In these citations, the underlined number appearing after the name of
he journal indicates the volume, and the second number indicates the page.
-exatplesLDAH102, 1097 -dhows that the article aPpearedin..DAN, volume
;F: page 1097. The number in parentheses is the year of publication. The
liv*erS following the citations tor Physical Abstracts indicate the abstract
ber. -in cases where an article, or an abstract of it has appeared in
her sources, they have aittio been 'listed. -
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Abrikosov, see Landau, L.D. Arzbany
'Co
Adirovich, E.I. and Podgoreckii, M.I.
"On the Interaction of Microsystems with Zero-point Fluctuations
an Electromagnetic Field," ZhETF 26, 150 (1954).
MR 16, 101 (1955) Phys Abs 9914 T1954)
Afrikyan, L.M.
"Multiple Pair Production in Quantum Electrodynamics," ZbEN 33,
531 (1957) 'ATV 6, 414 (1958)
"On the Theory of Creation and Annihilation of Anti-protons,"
naETF. 30, 734 (1956) A: 1, 443 (1957)
"Theory of the Production of Electron Positron Pairs in Collisions
of Slow - Mesons with Nuclei," 'UM 331 280 (1957)
JETP 6, (1958)
Akhiyezer, A.I. (also Akhiezer)
"Diffracted Radiation of Photons by Particles with Spin 1/2,"
DAN 94, 651 (1956). MR 160 514.8(1955)
Phys Abs 1892 (1957)
or
and Polovin, R.
"Radiative Corrections to the Scattering of Electrons by Electrons,"
DAN 90, 55 (1953). Days Abs 8223 (1953)
"Removal of Divergencies in Quantum Electrodyrumnice�" UFN 51,3
(1953). MR 16, 317 (1955) NSA 1264 (1954)
and Aleksin, V., and Volkov, D.
"On Some Effects Resulting from the Interaction of an Electromagnetic
Field with a Vacuum of Scalar Charged Particles," DAN 104, 830
(1955). NR 11, 1034 (1956)
Alekseyev, A.I.
-"Covariant'Equation for Two Annihilating Particles," JETP
696 (1957) NSA 12, 8 (1958)
Aleksin, see Akiezer
Aleksin, V.F., and Volkov, D.V.
"Radiation Corrections, to Particle Scattering in External Field
�
and to Compton Effect in Scalar Quantum Electrodynamics,"
Z1ET111- 33, 1044 (1957) JETP 6, 803 (1958)
"Interaction of the Electromagnetic Field with the Vacuum of Nuclear
Charge of Particles,' DAN 104, 830 (1955). NSA 1964 (1956)
- A45.
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Asanov
�
Averba]
----- a
Baadii
_ _ _ - �
Bare.
of.
)ns
ons,�
gnetic
830
aclear
5)
Approved for Release: 2022/03/16 C06927295
_EQB--OFFEKnal-17LY
Arzhamkh I.S.
"Coupled Systems of the Meson Field," DAN 110, 351 (1956).
Phys Abs 1903 (1957) A: 1631 .
MR 12, 365- (1958)
"Representation of the Meson Field by Retarded Potentials," DAN 110
953(1956). 'This Abs 3960 (1957) At 1792
NSA 3624 (1957)
MR 1.2, 2 (1958)
Askaryan,G.A.
On the Effect of the Oscillation of the Meson Shell of Nucleons
on the Probability of Particle Interactions," ZhBTF 26,
751(19511.) NSA1458.(1955)
Asanov, A.R.
� .1'Note Ond.Variant of Von-,Local .Field Equations," ZI5BTF 30, 619
� :(1956). Phys Abs 98 (1957)
Averbakh, B.L. (also Auerbach)
and Fradkin, B.S..
"Renormalizability of Pseudoscalar Meson Theory with.PseudOvector
� Coupling,"-7;h0TF]g)_,, 756 (1956); sup to 30,. no-4/7.
'-JETP 3)-862 (1957r :
MR 18,. 176 (1957) �
NSA-4206 (1957)
Phys'Abs -7121956)
Baldin,
"On a Rule for the Interaction of the Electromagnetic Field with
Nucleon and-Mesonic Field," NuovoCim III' series X,
no. I -(1956).
"Isotopic Invariance of7T-Meson Field" DAN 26.., 949 (1954)
NSA 6002 (1954)
and Mikhailov, V.
"On the Two Types of Charge Invariance," DAN 91, 479 (1953).
NSF, tr, 101 Phys Abs 3101 (1954)
Barashenkov,
"Compton Effects in the Extended Electron,"ZUTFf 71, 69411956)
JETP 4, 559 (1957)
"The Construction of a Phenomenological Scattering Matrix With Non-
local Interaction,"ZhETYF 32, 368 (1957) JETP, 5,313 (1957)
Phys Abet 7613 (1957)
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I ICJIL_GIWG-TakE7VSE�ONLY-
"Contribution to the Theory of Non-local Interactions," ZhETF 31,
837 (1956). Phys Abs 2975 (1957)
JETP 4) 5 (1957)
NSA 4) (1958)
A: 1773
"Some Observations on Possible Formulations of the Theory of
Exteuded-Particles," ZhETF 28, 579 (1955).
JETP 1, 467 (1955)
MR 17, 221 (1956)
NSA-6041 (1956)
Phys Abs 7694 (1955)
"On the Renormalizability of the Hamiltonian Formulation of Theory
with the Form-Factor," Nuovo Cim V, 1469 (1957)
"Concerning Some Possibilities of Formulation of a Relativistically
Invariant Theory of Extended Particles," ZhETF 32, 566 (1957)
JETP 5, 470 (1957)
NSA 12, 6 (1957)
and Barbasev, B.M.
"Statistical Weight of a System of Particles with Arbitrary Spins,"
Joint Institute for Nuclear Research, Laboratory of Theoretical
Physics - Nuovo Cim, sup VII, series X, no 1 (1958)
"Statistical Theory of Particle Multiple Production in High Energy
Nucleon Collisions." Joint Institute for Nuclear Research,
Laboratory of Theoretical Physics, Nuovo Cim, sup VII;
series IV, no 1 (1958)
"Electrical Polarizability of the Meson Cloud in a Nucleon," Joint
Institute for Nuclear Research - Laboratory of Theoretical
Physics, A: P-169 (1958) (Preprint)
Barbasev, B.M. see Barasenkov� V.S.
33.1Ye1, V.N.
and Pekar, S.I.
"Strong Coupling Nucleomesodynamics. II. The Ground and Isobar
States, Nucleon Charge and Spin," ZhETF 30, 317 (1956);
sup to 30, no 2,6.
JETP 3) 340-350 (1956).
MR 187 174 (1957)
NSA 2206 (1957)
Phys Abs 4836 (1956)
A: B-6
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Bazar�.
Belett
Be
Beret
mim as.
Bil
Ble
pproved for Release: 2022/03/16 C06927295
zoR-appieEe--usz-ower-
-Bazarov;
- 7EquatiOns with Variational Derivatives and Distribution Functions
for. Systems with Complex Interaction," DAN 1104 38 ,-(1956)..
Soviet Physics Doklady I, 520(1956)
Helen lkty; 5.2. .
"Connection Between Scattering and Multiple Production of Particles,"
..(1956). Nuclear Physics 1, 259 (1957)
"Theory of Multiple Production of Particles at Nigh Energy,"
ZhETF 28, 111 (1955). NSA 4025 (1955)
Landau, L.D..
"HydrOdyrami eche Theorie der. Mehrfacherzeugung von Ten:Oen:1-n
UFN 565 309 (1955) Fort derPhyS.UY 6(i1955).
Belyayev, 2 S.T.
and Budker, G.I.
"The Relativistic Kinetic Equation," Proceedings of the .AtadeMy of
Sciences i-USSR� 107, 6 . (1956) ,Soviet Physics Doklady 2(1956)
Bereptetskiy, VB., (also Beresteckii, V.B.)
"Asymptotic Behavior of Electromagnetic Polarization of the Vacuum
in the Presence of Meson Interactions 1 n:Zh$17. g25.. 585 (1955).
dETP 2, 540 ( 1956 )
MR 17; 92a . (1956) -
Phys Abs 2638 (1956)
and ByOkkov,
..11-Meson Scattering with Change of Intrinsic 'Parity,": Nuclear,
,Physics 3, 153-156 (1957) .
and Kroklin, O.N. and Xhlebnikov, A.K.
"Radiative Correction to the Magnetic Moment of the u-meson,"
ZhETF 22, (1956). Phys Abs 7127 (1956)
Biletkiyi S.M., see BogolyUbov, N.N.
Blank, V4 21 a
6.Behavior of the Green's Function of the Electron for Small Momenta,"
DAN 104, 706 (1955). MR 17, 1032. (1956)
"Behavior of the Vertex Part at High Energies,." DAN 12/, 389 (1956).
Phyli; Abs 4810 (1956).
"Application of a Renormalized Group to, Different Scattering Problems
in Quantum Electrodynamics," ZhETF: 2aL, 932 (1957) JETP
759 (1957)
NSA 12 no. 8 (1958)
Phys Abet 8378 (1957)
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� �20,11-colneak-L--tm7orrr-
and Shirkov, D.V. (also Sirkov, D.V.)
"Asymptotic Investigation of Vertex Part in Quantum Electrodynamics,"
DAN 111, 1201 (1956). Phys Abs 5040 (-1957)
"Inverse Dispersions Relations," ZhETF 33, 1251 (1957)
JETP 6, 962 (1958) (Preprint)
"Improvement of Quantum Electrodynamics Perturbation Theory with
Help of Renormalization Group." Nuclear Physied 356 (1956)
Phys Abs 5829 (1957)
and Bonch-Bruevicht V. L., and Shirkov� D.V.
"Remarks on the Multiplication Renormalization Group in Quantum
Theory of Fields," ZhETF 33, 265 (1957)
JETP �.� 204 (1958)
Phys Abs 61, 724
NSA 8894 (I.958)
Blokhintsevi D.I.
"A Non-Hamiltonian Method in the Theory of Elementary Particles,"
ZhETF 12, 266 (1947)
"Non-Linear Field Theory and the Theory of Relativity,"
Nuovo Cim, III, sup 629 (1955)
"Non-Local and Non-Linear Field Theories," UFN L(1957)
NSA 7381 (1957)
Phys Abs 5840 (1957)
"Theory of Nucleons" ZhETF 29, 33 (1955).
JETP-2, 23 (1956)
Phys Abs 8496 (1955)
"When Does a Weak Interaction Become Strong?" Joint
Nuclear Research (1957) NSA 12, no 2 (1958)
"On a Possible Limit of the Applicability of Quantum
Joint Institute for Nuclear Research (Preprint)
A: P-148 (1958)
Institute of
Electrodynamics,"
BogolyUbov, N.N.
"Casual Operators in Quantum Field Theory," DAN 99, (1954)
"Condition of Casuality in the Quantum Theory of Fields," IAN151.,
237 (1955). NSA 7595 (1955)
_EDB�CiLEFIG-I*L-1:18E-01=
Approved for Release: 2022/03/16 C06927295
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.01;t_cggpie-BEL--usg--ority-
"Equations with Variational Derivatives in Problems of Statistical
Physics and Quantum Field Theory,!' Moscow State University 10,
no 4-5, 115-124 (1955). Phys Abs 5817 (1957)
-
"Fotuidation'of-RelatiVistic--QUantum-Field� Theory, DAY'S', 757(1951)
Abhandlungen aus der Sowjetischen Physik, Folge IV, p7-10.
NarlagACUltur and FOitschritt, Berlin', 19511. MR 11,-71 (1954)
MR 1D 112 (1956). -(GaMan tt) .
"On Representation of Green-Schwinger Functions by Means o
Functional Integrals," DAN 22.225 (1954).
MR 16, 778 (1955)
Phys Abs /954 (1956)
"On a New Form of Adiabatic Perturbation Theory in the Problem of
Particle Interaction with a Quantum Field," Ukran Mat Zh, 2.
MR 19, no 3 (1958)
"On a Variational Principle in the Many-body Problem DAN, SSSR
119, 244 (1958), Phys Abs 3719 (1958)
and Parasyuk, O.S.
"On the Analytic Continuation of Generalized Functions," 1225
717 (1956) (Preprint)
MR 11:5 404 (1957)
"!On'the�TheOr'df Multiplication Of Causal Singular Functions,"
DAN 100, 25 (1955).
MR 1/, 112 (1956)
Phys Abs 7955 (1956)
"On he SUbtractivaTormaliam in Multiplication of Causal Singular
Functions," DAN 100, 429 (1955)
MR 17, 112 (19563-
Phys Abs 7956 (1956)
and Shitkov, D.V. (also Sirkov, D.V.)
"Appiitation' of the Renortalization Group to ImprciVement of Formulas
in Perturbation Theory," DAN 103, 391 (1955).;- � ' -
PM 1 441 (1956)
NSA 02 (1957)
Phys Abs 8a:-(1957)
"Charge Renormalization Group in Quantum Field Theory," NUovo Cim
(1o) 2) 845 (1956)
MR 1p 1260 (1956)
Phys Abs 11.805 (1956)
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"A Model of Lee Type in Quantum Electrodynamics," IAN 105, 685 (1955).
MR 17, 1033 (1956)
"Multiplicative Renormalization Group in Quantum Field Theory,"
ZhETF 30, 77-(1956). MR 2./1 1260- Phys Abs 11.806 (1956)
"The Multiplicative Renormalization Group in the Quantum Theory of
Fields," JETP 3/ 57 (19561 MR 18, 1106-(1957)
"Problems in the Q1223.MtUM Theory of the Field," UFN 57, 3 (1955).
Phys Abs 11.182 (19561-
"Problems in Quantum Field Theory," UFN 55, 149 (1955). NSA 11.907
(1955) Phys Abs 902 (1956)
"On the Renormalization Group in 'Quantum Electrodynamics," DAN 103,
203 (1955). MR 170 441 (1956) NSA 720 (1955) Phys Abs '81-T1957)
and S:hirkov, D.V.
"Problem der Quantem feld Theorie," UFN 52, 189 (1954)
Fort d Phys 4, 438 (1956)
"Problems der quantem-theorie. der Felder,
Fort d Phys 3, 439-495 (1955)'
and Zubarev�-D.N.
"Wave Functions of Lower States of Interacting Bose Particles Systems,'!'
ZhETF-28 129(1955)
UFN 55�, 3-49 (1955)
and V.S. Vladimirov
"On the. Analytic Continuation of Generalized Functions," (1957)
(In Russian) Ar. Joint Institute. of Nuclear Research (Preprint)
and Bilenkyl S.M. and Logunov, A.A.
"Dispersion Relations for Weak Interactions," Nuclear Physics 5,
'no 2 383389 (1958)
"Dispersion Relations in the Case of Weak Interactions," DAN 1151
891 (1957) Phys Abs 2789 (1958) (Preprint) . -
and Nedvedev, B.M. and Polivanov,
"On the Indefinite Metric in Quantum Field Theory," Dana, 1958.
Joint Inatitute for Nuclear Research A: P-176 (Preprint)
-A51-
2.4E-DEEIGEM:re&E-ONLT-
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Bc
Be
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1955).
of
LO3,-
-(1957)
ystess,
Approved for Release: 2022/03/16 006927295111MIIIIIIIIIIMP
FOR OFFICIAL USE ONLY
and Medvedev, B.V. and Polavamov, M.K. and Shirkov, D.V.
"Problems of the Theory of Dispersion Interrelationships," Joint
Institute of Nuclear Research, Dsboratory of Theoretical Physics
(1957) NSA. 12, no 2 (1958) (Preprint)
Bonch-Bruyevich0N.L. (also Bonc-Bruevic, V.L.)
"Adiabatic Approximation in the Theory of the Green' Function,"
DAN 105, 689 (1955). MR 17,1032 (1956)
"Spectral Representation of the Green's Function in the Non-
relativistic Many-body Problem," ZhETF 31, 522 (1956).
JEW 4, 4.56 (1957) Phys Abs 1885 (1957) A: 1664
and Nedvedev, B.V.
"The Bringing of the Product of Operators to Canonical Form in the
Theory of Second Quantization," ZhETF ?2, 410 (1953).
Phys Abs 39 (1955)
"On the Invariant Construction of a Quantum Theory of Fields. II."
ZhETF 22, 425 (1952) MR 140 227 (1953)
NSA 1307 (1953) �
Bonch-Bruevich, V.L. see Blank,
Bonch-Bruevich, V.L. see Medvedev, B.V.
Borgardt, A.A.
"On the Theory of Meson Fields. I. Vector Field of General. Type in
. � the .Vacuum," ZhETF 24, 24 (1953). NSA 7190 (1954) Phys Abs 9918
(1954)
:"On theJTheory.of Meson Fields, II. Field with Sources," ZhETF 24,
Tint) 284 (1953). NSA 7191 (1954) Phys Abs 9919 (1954)
"On the Theory of Meson Fields. III. Conservation of Physical
Quantities," ZhETF 30, 330 (1956); Supplement to 30, no
MR 96 .(1957)175k2207.(1957) Phys Abs 11.837 (1956)
� "The Gravitational Self Energy of Particles in the Classical Field
Theories," ZhETF 28, 377 (1955) JEW 1,380 (1955). NSA 2958)
(1955)
"Matrix Aspects of the Theory of Bosons." ZhETF 30, 334 (1956);
sup to 30, no 2,6. MR 18, 96 (1957)
809:(1957) PhysAbs-4851.(1956)
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"Ncin7linear Meson Field.of:aNucleon at Rest," DAN 1091, 1107(1956)
Phys Abs 1901 (1957)
MR 19, no 3 (1958)
"NOn-linear ikis011 Field Equations," ZhETF 33,-60 (1957).
JETP- 6, 43.(1958)
NPA 81689 (1958) -
Phys Abs 2800 (1950
"Pseudoscalar Interaction in.Non-linear-Mesodynamics," DAN 110,
42 (1956) Soviet Physics Doklady 10 624 (1956)
Phys Abs 1902 (1957)
A: 1475
NSA 7614 (1958)
Borovikov, V.A.
"One Topological Problem Connected with Problems in Quantum Electro-
dynamics," Uspekhi Matem. nauk. 11 no 3, 113-118'..(1950.
A: B-5
Brodskiy,
"General Theory of Meson Scattering," DAN 111, 787 (1956).
Phys Abs 3963 (1957)
MR 18, 10 (1957)
"On the Derivation of the Low Equation in the Theory of Meson
Scattering," ZhETF 32, 616(1957) -
JETP 5, 509 (1957)
Phys Abs 61, 721 (1958)
"Problem of Renormalization in Nesodynamics," DAN 105, 939 (1956).
MR 17, 1034 (1955)
Phys Abs 1062 (1957)
and Ivanenko, D. and 'forst, N.
"Difference of Messes of Elementary Particles," DAN 105, 1192 (1955).
MR 18, 97 (1957)
Brodskiy, A.M. see Ivanenko, D.
Budker, G.I. see Beliaev, S.T.
Buymistrov, V.M. and Pekar, S.I.
"Quantum States of Particles Coupled to a Harmonically Oscillating
Continuum with Arbitrary Strong Interaction, I"
"Case of Absence of TranelationalSymmetry," ZhETF 32, 1193 (1957)-
JETP 5, 970 (1957)
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otro-
Approved for Release: 2022/03/16 C06927295
-r-DR-012FIGSkt-tISE-ONEY-
Byckkov, Yu. AL. see Beretelsky, V.B.
Chang Lee
"Stationary States of Electron-Positros Systems and Annihilation
Transitions," ZhETF 33, 365 (1957)
JETP 6, 281 (1958)
Chavehanifte,
"On the Equations of Quantum Electrodynamics," Soobac. Akademii
Nauk Gruzin SSSR 17, 15 (1956)
MR 18, 174 (1957)-
"On the Interaction of Boson-Fermion Fields, DAN 104 205 (1955).
MR 17,811 (1956)
NSA 1160 (1956)
Chernanskiy,-D.S.: see Feinberg) E.L�
Chod KUAng Ch:adand M.I. Shirokov
"Relativistic Theory of Reactions Involving Polarized Particles,"
(1958) (In Eng11s0
A: P-122 Joint Institute for Nuclear ResearekOreprint)
Companests, A.S. (also Kompaneets, A.S.)
,"Equation of, Self Consistent Fields for 'Nuclei by Calculation: of
Electrostatic Force,"ZhETF 26, 153 ,
NPA 456 (1955).
"On the N Formulation of Electrodynamics by Dirac," DAB 82,
873 (952').'.
Phys Abs 51;.50(].953)
ovic, V. see Ivanenko, D.
Demkov, Yu. N., (also Denkov)
"Principle of Detailed Equilibrium in Quantux Mechanics and
13-955). Certain Homologies for Scattering Amplitudes in the Theory
of Collisions," DAN 2/0 1003 (1954)
Delginbv,
"Relativistic Spherical Functions," ZbETF 30 746 (1956).
Al B-6
DUen-I,Shi
ring -----ICT�Sneralized'RegUlar Solutions for a Point Charge in General-
relativistic Scalar Meson-field Theory,'" ZhETF.31k 1089 (1956).
51)
Phys Abs 5071 (1957)
-F-011-0,17-19var�e5LP-mrs-
A r,r,rnuRrI for Release: 2022/03/16 C06927295_ -.
pproved for Release: 2022/03/16 C06927295
"General Covariant Covariant Formulation of the-Field Theory and General. �iaw.
of Conservation," Joint Institute of Nuclear Research, Laboratory
of Theoretical Research. lip. (1957)
NSA 12, no 2 (1958)
DyatloV1:14. and Ter-Martirosyan,
"Asymptotic Theory of the Scattering of Mesons by Mesons," ZhETF 301
416 (1956).
Phys Abs 5702 (1956)
A: B-6
Sudakov, V.V. and Ter-Martirosyan,
"Asymptotic Meson-Meson Scattering Theory," ZhETF 32, 767 (1957)
JETP 5, 631 (1957)
Dykman, LPL and Pekar, S.1.
"Strong Coupling Nucleomesodynamics, III. Translational Motion,
Meson-field Mass and Nuclear Magnetic Moment," ZhETF 30, 1125
(1956).
JETP 3, 882 (1957)
NSA 4207 (1957)
Phys Abs 8593 (1956)
Eleonskii, V.M. and Zyrianov, P.S.
"Contribution to the Theory of ColleCtive Motion of Particles in
Quantum Mechanical Systems," JETP 5, 432 (1957)
NSA 12, no 6 (1958)
"Application of the Hartree-Fock equations to a system of Quasi
Particles," ZhETF 33, no 1, 289-91 (1957)
Phys Abs 724 (1958T
Faddeyev, L.D.
"Uniqueness of Solution of the Inverse Scattering Problem," Vestnik
Leningrad University 111, no 7, 126-130 (1956)
MR 18, 259 (1957)
Faynberg, V. Ya. (also Faynberg)
"Non-linear Equations in Quantum Field Theory," ZhETF 30, 608 (1956).
MR 18, 176 (1957)
NSA 2216 (1957)
Phys Abs 7965 (1956)
"On the Theory of Excited States of Nucleons 1., II," ZhETF 25,
636, 644 (1954).
Phys Abs 2408, 2409(1955)
�F-033--01T4G-9i�ussr-Olirr
Approved for Release: 2022/03/16 C06927295
Fainb,
Fedja
Fedor
Fe
Fil:
Fis
FrE
tory
vo,
6
: .201Lagg-iglAi2-ust7oN1�
and Fradkin, E.
"Dispersion Relations for Fermi Particles," DAN 109, 507 (1956).
Soviet Physics Doklady 1, 455 (1956)
NSA 1706 (1957)
Phys Abs 1055 (1957)
A: 1431
Fainberg, V. Ya. see SiIin, V.P.
Fedjanin, V.K. and TaVillieiidze A.N.
�.:.-"Approximate Equations for 13roton Scattering Amplitude on Nucleons,"
Joint Institute for Nuclear Research (1958)
A: P-I25 (Preprint)
Fedorov, F.I.
"Reduction of Wave Equations for Spin 0 or 1 to the Hamiltonian
Form,"-ZhETF 34 140 (1956) �-
Phys Abs 1078T1957)
JETY If, 139 (1957)
Feynberg, E.L. and Chernayskiy, D.S.
"Higher Approximations in the Self-Consistent Field Method of
Meson Theory," DAN 108, 619 (1956)
Soviet Physics Doklady 1, 354 (1956),
"Deuteron Stability in Meson Theory," DAN 103, 589 (1955).
. NSA 1137 (1956)'
Filimonov� G.F. and Shirokov� Yu. M. (also Sirkovl Yu. M. and Shirkov, Yu.M.)
"Plural Interaction Hamiltonian in Quantum Electrodynamics,"
ZhETF 321, 99 (1957),
JETP 5, 84-88 (1957)
Phys Abs 5041 (1957)
'Fischer, J.
"Equations for the Green Functions in Quantum Electrodynamics,"
- (1957) (In English) Joint Institute of Nuclear Research (Preprint)
Fradkia, E.E.
-"Particle with Spin 3/2 in an Electromagnetic Field," ZhETF 32, 363
(1957)
JETP,5� 298 (1957)
Phys Abs 7599 (1957)
"On the Rarita-Schwinger Method in the Theory of Particles of Half-
integral Spin," (1957).
.TEIT 2,1203 (1957)
APhYs Abs 2148 (1958)
ZhETF 32, 1479
- A56 -
-FOR�OPPIGEPrErif833--effiff�
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_EMLOWLIGEitrL-7USE-VNEY-
and Izmirilov, S.V.
"On the Permissible Transformations of Equations. for Particles-vt
Higher Spins," DAN 114, 277 (1957).
Phys Abs 9003 (19573�
Fradkin, E.S.
"Concerning Some General Relations of Quantum Electrodynamics,'
ZhETF 29, 258 (1955)
JETP (1956)
"On the Asymptotics of Green's Functions in Quantum E1ectrodynaM164
ZhETF 28, 750 (1955).
MR 17,333 (1956)
Phys Abs .p4.9,74 57)
"Dispersion Relation for Axbitrary. Scattering," MEW, 21/ 515 (1956%
JETP 4, 450 (1957)
Phys Abs 3974 (1957)
A: 1655
"Green's Functions for the Interaction of Nucleons with Mesons,
DAN 98, 47 (1954).
MR 167 317 (1955)
Phys Abs 7987 (1956)
"On the Problem of Asymptotic Green's Function in Meson Theory with
Weak Pseudoscalar Coupling," ZhETF 29, 377 (1955).
JETP 2, 340 (1956)
NSA 9718 (1956)
Phys Abs 915 (1956)
"On the Problem of Interaction of Two Quantum Fields," DAN 1000
897 (1955).
MR 17, 219 (1956)
NSA7030 (1955)
Phys Abs 7991, (1956)
"On Quantum Field Theory. I," ZhETF ?.2) 121 (1955).
MR 22, 219 (1956)
NSA 7598 (1955)
Phys Abs 8485 (1955)
"On Renormalization in Quantum Electrodynamics," ZhETF 26, 751 (1954).
MR 16 317 (1955)
Phys Abs 44 (1955)
"On Some General Relations in Quantum Electrodynamics," ZhETF ?,25 no 2
(8), 258-261 (1950
Phys Abs 59 (1956)
-A57-
_EDEL-OPFIGEtizfr-USE-TNL"r
Anoroved for Release: 2022/03/16 C06927295
fracuti
ith
1956).
ith
1954).
2 no 2
Approved for Release: 2022/03/16 C06927295
Fradkin E.S. see Avrorin, and Fainberg V. �
.Frenkelt4-11::. (now deceased
"Remarks on Quantum Field Theory of 'Matter," UFN 42 69-75 (1950
Galanin, A.D.
"On the Expansion Parameter in the FteUdoscalar.Meaon. Theory with
PseUdoscalar Coupling," ZhETF 26, 417 (1954).
.(1955) . �
ThytAbs 53-(1955)
-NsA-2089-(1955)---
"On the Possibility of 'Formulating a Meson Theory with Several
'Fielda,"-ZaTF 5, 460 (1957)
NSA 12, no 6(1958) .
ZhETT-2L03 552-558 (195r)
"Convergence of the Perturbation Theory Series'fOr-a Non-relativistic
Nucleon," ZhETF 33, 285 (1957)
ans�61 221 (195E7-
"RadiatiVeCorrectiont�in QuantuMElectrodynamics.-I II," � ZhETF 22,
448, 482 (1952).
MR 14, 436 (1953)
NSA 1300 (1953)
,�.
"Relativistic. Equations of Interacting-Particles," ZhETF 22, 448
. (1952).
NSA 763 (1954)
"A Relativistic Equation of Interacting Particles-" .ZhETF 23, 488
(1952). �
MR 111, 707 (1953)
Phys Abs 5298 (1953)
"Some Remarks on Divergences in the Theory of a Fteudoscalar Meson
with PseudovaCtor Coupling," ZhETF 26�.423 (1954).
MR 16, 888 (1955)
NSA 2090 (1955)
Phys Abs 5k (1955)
and Lapidus, L.I.
"Observations on Mixed Meson Theories," ZhETF 31, 359 (1956).
Phys Abs 3973 (1957)
A: 1449
- A58 -
_20.11-01EFIGIAL--1182-ONET-
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pproved for Release: 2022103116C06927295
-seR-epple-Liks-uSE-ONEY-
and Iciffel B.L. and Pomeranbhtk, I. Ya.
"On the Asymptotics of Green's Functions of a Nucleon and Meson-
in-the Pseudoscalar Theory with Weak Coupling,' ZhETF
(1955).
MR ID 44o (1956)
NSA 7597 (1955)
Phys Abs 1070(1957) �
"Renormalization of Mass and Charge in the Covariant Equations of
Quantum Field Theory," DAN 21 361 (1954).
MR 160 547 (1955)
NSA 2042'(1955)
Galanin, A.D. see Abrikosov
Geylikman, B.T.
"On Polarization of the Vacuum in the Theory of Strong Scattering,"
DAN 21) 225 (1953).
MR 15, 918 (1954)
Phys Abs 6287 (1954)
"On the Quantum Theory of Wave Fields," DAN 90, 359 (1953).
MR 15, 379 (195)4)
NsA-5452 (1953); NSA 464 (195)4)
Phys Abs 8233 (1953)
"On the Theory of Strong Coupling for Meson Fields," DAN 90, 991
(1953).
918 (1954)
NSA 157 (1954); 5661 (1953)
Phys Abs 3100 (1954)
On the Theory of Strong Coupling," DAN 91, 390 (1953).
MR 15, 918 (195)4)
Phys Abs 6286 (195)4)
"On the Theory of Strong Coupling for Meson Fields I, II," ZhETF 25,
417, 438 (1955).
JETP 2, 601 (1956); 509 (1956)
MR 1771162 (1956)
Phys Abs 916, 917 f1956)
"On the Theory of Strong Coupling for Meson Fields. III," ZhETF 2j)
572 (1955).
JETP 2 451 (1956)
MR 17, 1163 (1956)
Phys Abs 918 (1950.
-A59-
-EOR-QFF-IGEkL�UBE-ONL'T-
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Geiz
�Gelf
_ - -
WM!
Gir
Gd.
2
?9:
Approved for Release: 2022/03/16 C06927295
AlaPielBE-01Mr
"Quantum Theory of Distributed Fields," DAN 90, 359 (1953).
NSA 5452 (1953)
Geizenberg, V. (Heisenberg, Werner)
4The Contemporary Interpretation of the Element Particle Theory,"
IAN 60, 413 (1956)
NSA 3729, (19'57)
1:4
Gelfand, I.M. and Minlos
"Solution of the Quantum Field Equations," DAN 21, --213 (1954),
.TtanS1ated-MR�161 315-(1955) .
and Yaglom,
"Integration in Function Spaces and Its Application :to Quantum
Physics,":usephi Mat..Nauk 11, 77-114(1956). �
MR 17, 3.261 (1956)
ainzburgl,
"On.EmPrgentefrom the: Region of Weak: Coupling in the ,Two-charge
Meson Theory," DAN 110, 535 (1956).
Soviet Physics Doklady 1, 560 (1956)
Phys Abs 1904 (1957)
'A: 1644
NSA 7615 (1958)-:
Phys Abs 1904 (1957)
and Shirkov,
"Asymptotic Behavior of Higher Green's Functions," joint Institute for
Nuclear Research, March 1958. (Preprint)
Ginsburg, V.L. and Tam, I.E.
"On the Theory of Spin," Translated by G. Belkov. National Research
Council of Canada, Ottawa. Tech. translation TT-305, 23 pp.
(1952). ZhETF 17, 227 (1947); MR 14, 839 (1953)
Gol'fand, Yu. A.
"Construction of Propagation Functions by the Method of Quasi-fields,"
ZhETF 28, 140 (1955).
MR 17, 221 (1956)
Phys Abs 5214 (1955)
"Fermi Fields and Spinors of Infinite Span," DAN 13, 68 (1957).
NSA 8238 (1957)
"Transformation Properties of the Electron-positron Field Amplitudes,"
ZhETF 31, 535 (1956).
JETP 47461 (1957)
Phys Abs 1917 (1957)
-A60-
2213-DREW-V.12-146:2-eitrr
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pproved for Release: 2022/03/16 C06927295
�FOR--OFF-I-01*L-115DVNEY�
"Generalized Phase-shift Analysis as a Consequence of the Unitary of
the Smatrix," ZhETF 31, 224 (1956).
Phys Abs 1916 (1957)
GolUbenkov, V.N. and Smorodinskik,
"The Lagrangian Function for a System of Identically Charged PartiCleaii
ZhETF 310 330 (1956).
JETP.471142 (1957)
Gor'kov, L.P.
"On the Asymptotic Form of the Green's Function of an Electron,"
DAN 105, 656 (1955).
MR 17,1033 (1956)
"Green's Function of Charged Particles in the Region of the Infra-red
Catastrophe." ZhETF 22, 790 (1956).
Phys Abs 7132 .(1956)
"Two Limiting Momenta in Scalar Electrodynamics," ZhETF 32,
(1957).
JETP 5, 167 (1957)
Phys Abs 5830 (1957)
359
"Determination of the Phase Shifts Of the Matrix Elements of the
S-Matrix," ZhETF 33, 1431 (1957).
NSA 12, no 9 (195gT
and Khalatniko*,
"Asymptotic Behaviour of Green's Functions in the E1ectrodynAl,711,r5 of
Particles with Spin Zero," DAN 104, 197 (1955).
MR 17, 566 (1956)
"Electrodynamics of Charged Scalar Particles," ZhETF 31, 1062 (1956).
JETP 4, 777 (1957)
Phys Abs 2969 (1957)
A: 1885
"Perturbation Theory and Asymptotic Behavior of Green's Functions in
the Electrodynamics of Particles with Spin Zero," DAN 103,
799 (1955).
MR 121, 566 (1956)
NSA 1139 (1956)
-A61-
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Grig(
Gure.
Gurz
Hal
Bet
of
cles,"
red.
Approved for Release: 2022/03/16 C06927295
1:OLDEEIG-ITArT:ri5ST-131Trr
Grigoryev,-V.
-,'"GeneraliZedAethOd'of Calculation of Damping:in:the Quantum.Theory
� of Fields," ZhETF 25, 40 (1953).
Phys Abs 42 (1955)
"Generalized Method of:Calculation of Damping in Relativistic.
Quantum Field Theory?"ZhEN.301. 873 (1956).
Phys Abs� 8003 (1956)
JETP 3s 691 (1956):
MR 125 nO 2 (1958)
"Quantum Field Theoretical Solutions Without Perturbation Theory,"
. ZhETF-.. 146: (1957)-
JET!' 5?,109119581:
"On the Question of Role of Nuittng in the Theory of Bound Particles,"
ZbETF 25, 51 (1953)'
Thys.Abs-43 (1955)
"Solutions in Quantum Theory of Fields without Recourse to Perturbation
� Methods," ZhETF 32,. 146 (1957).
Phys Abs 5874 (1957)
Grigoryev, :V.. I. see �Ivanenko, D.
Gurevich, A.V.
"Quantization of Fields Obeying Equations with Higher Derivatives II"
ZhETF 24, 149 (1953).
'Phys Abs 9920 (1954)
NSA 7193 (1954)
Gurzhi� R.N.
"On the Scattering of Photons by Nucleons,"
6). JEW 3, 941 (1957)
Halatnikov, I.M. (see other spelling: Khalatnikov)
Baffin, L.A. (see also Khalfin, L. A.)
in "Physical Invariance of Quantization," Vestnik Leningrad University 11,
no 22, 12 (1956)
MR 19, 362 (1958)
Heber? Von G.
"Messprozess und Algebraische Eigenschaften der Feldgrossen in
einer Einfachen Model-Feld Theorie," Vereingtes Insitut fur
Kernforschung Laboratorium fur Meoretische Fhysik
A: P-150 (1958) (Preprint)
-A62 -
_EM-CALF-I-C4A-L-115%-ONLY-
oproved for Release: 2022/03/16 C06927295
Ninpu.A.Aning Hu)
"The Proper Meson Fieldof a..Physical Nucleon," Joint Institute for.,
Nuclear Research
A: P-87 (1957)
pproved for Release: 2022/03/16 C06927295
..5_3113_0=Critkiritalt-13NET
Ingarden R.S.
"On a New -Type of Relativistically Invariant Linear Local Field
Equations," DAN 108, 56 (1956).
Soviet Physics Doklady 10 256 (1956)
MR 18, 542 (1957)
Phys Abs 713T (1956)
"Equations of Motion and Field. Equation in the Five Dimensional
Unitary Theory of Relativity," DAN 88, 773 (1953)
NSA 5220 (1953)
Ioffe B.L.
'Dispersion Relations for Scattering and Photon Production," ZhETF 21,
538 (1956).
JETP 4, 534 (1957)
Phys liths 3721 (1957)
A: 1888
"On the Divergence of a Perturbation-Theory Series in Quantum
Electrodynamics," DAN 940 437 (1954).
NR 15, 917 (1954)
Phys Abs .2989 (1957)
"Systems of Covariant Equations in Quantum Field Theory," DAN 95,
761 (1954).
MR 16, 100 (1955)
NSA-4468 (1954)
Phys Abs 5034 (1957)
and Rudik, A.
"On the Decay of the Pi-Meson," DAN 82, no 3, 359 (1952).
Phys Abs 5099 (1953)
and Pomeranchuk, I.Ya. and Rudik, A.P.
"DisperSion Relations for Scattering of Pi-Mesons by Deuterons,"
ZhETF 31, 712 (1956).
JET? 47588 (1957)�
Phys Alps 3002 (1957)
A: 1895
Ioffe, B.L. see Galanin0 A.D.
A63: -
_EDE--417-14-TAL�tra�ONLY-
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Ivanex
... ���
IVE
>r
21,
Approved for Release: 2022/O3/16 c0927295
.-F-013--037-1-GEartierVITLY-
Ivanenko, D.D.
"Introduction to the Theory of Elementary Particles, Part II,"
UFN" 32, 261 (1947)
and Brodskiy: A.M.
"Divisible Processes and Non-linearity in thef-Theory of: Elementary
Particles,!' DAN 84, 683 (1954.
Phys Abs 5300-(19.3)-
� InteractiOn Of Gravity witbJVacUum Particles1".DAW92 731-(1953)
MR 16/ 547-(1955)
NSA 1767 (1954)
Phys Abs -(1954)
� "On s. Non-linear Quantum Theory of the Electron:." ZhETF 24, 383
(1953).
Phys Abs 48 (1955)
and Cytovic,'
"The -Relativistic Equation of Three Coupled Bodies:" DAN 99, 373
(1954).
MR 16, 982 (1955)
Phys Abs 8581 (1956)
and Grigoryev, V.I.
"On the Interpretation of Regularization Procedures in Quantum
Electrodynamics," ZhETF 21, 563 (1951)
and Kolesnikov, N.
"The Electrino Hypothesis," DAN 87, 923 (1952).
MR 14, 828(1953)
Phys Abs 3083 (1954)
NSA 3650 (1953)
Ivanenko, D.D. and Kurdgelaidze, D.F.
"The Basic Equations of Mesodynamics," DAN 96, 39 (1954).
MR 16, 887 (1955)
NSA-5460 (1954)
Phys Abs 7988 (1956)
and Lebebev, V.
"Multiple Processes in Interactions," ZbETF 22, 638 (1952
Phys'Abb:618 .(1953)
-A64-
10_91i7.1,C1.412-1:19E-ONEY-
Li nnrnved for Release: 2022/03/16 C06927295,
pproved for Release: 2022/03/16 C06927295
jaLSZEICIAL-03E-ONEr"
and Mirianasvili, M.
"Nbn-linear Generalization of the Dirac Spin or Equation,
413 (1956).
Soviet Physics Doklady 1, 67 (1956)
MR 2,8, 95 (1957)
Phys Abs 6350 (1956)
A: 1B-6
and Sokolik� G.
"The Theory of Particles of Arbitrary Isotopic Spin and the Methoa
of Fusion," DAN 97, 635 (1954).
MR 16, 888 (1955T
Phys Abs 7979 (1956)�
"Unified Description of Ordinary and Isotopic Sparer"
Nuovo Cim 6, 226 09571-
and Kurdgelaidze, D.F. and Larin, S.
"Remarks on Non-linear Mesodynamics," DAN 88, 245. (1953).-
MR 11.1) 827-(1953)
NSA-4996 (1953)
Phys Abs 6471-(1953)
Ivanenko, D. see Brodskii, A., Sokolov, A.A.
Izmirilov, S.V.
"On the Relativistic Quantum Theory of Particles with Internal
Rotational Degrees of Freedom," ZhETF 629 (1947).
NSA 11.292 (1953)
Izmirilov, S.V. see Fradkin, E.E.
Kalitsin, N.S.
"On Certain New Methods of Eliminating Divergencies in Quantum
Electrodynamics," Ref. Zhur - Fizika, no 2 (1957)
no '2949 A: B-5
"On the Five-dimensional Theory of Nuclear Interaction and a New
Solution of the Dipole Difficulty," C.R. Acad. Bulg. Sci 7,
no 3, 1-5 (1956).
Phys Abs 74 (1956)
"On the Interaction of an Electron with the Fluctuations of the
Electro-Magnetic Field in a-Vacuum," ZhETF 22, 407 (1953).
Phys Abs 2406 (1955)
- A65
FO___ILQEE.T.Cakir455"E-ONLY-
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11
-rpm=
Kase
Ker
Kha
Approved for Release: 2022/03/16 C06927295
13_0=G-TairL�USE-Olfrir
"A New Variant of Equations of the Meson Vector Theory," ZbETF 24,
W6, '.293.(1953).:
Phys Abs 8011.k (1954)
hod
72
Karpman�
"On
a-Connection Between the Method; of Regularization and Theories
of Particles with Arbitrary Spin," DAN 892 257 (1953).
1R-152-379-(1954) '
: NSA '397k (1953) and 5450.(1953)
Phys Abs:7444'(1953)
"Quantization of Wave Fields with Finite N.-Umber of. omponents,"
ZhETF 21, 1337 (1951)
"On the S-natrix for Particles with Arbitrary Spin," ZhETF,E5
1104 (1956).
JETP-1, 934 (1957)
NSA 11.209 (1957)
Phys Abs 8602 (1956)
A: 1410
Kaschluhn, F.
"Impulse Approximation and Dispersion, Relations' for Pion-Deuteron
Scattering," Joint Institute for Nuclear Research
A: P-198 (1958) (Preprint)
"Dispersion Relations for Pion-Deuteron Scattering 112" 'Joint
Institute for Nuclear Research,
A: P-183 (1958) (Preprint)
Kerimov, B.K. see Sokolov, A.A-
Khalatnikov2 I.M. (Also Balatnikov)
"Concerning the Elastic Scattering of High Energy Particles,"
Institute for Physical Problems, Academy of Sciences, USSR,
(1957)
Nuclear Physics 32 433 (1957)
"Representation of Green's Function in Quantum Electrodynamics in the
Form of ContinuOus Integrals." ZhETF 28, 633 (1955).
JETP 12.568 (1955)
MR 177,-332 (1956)
NSA-6092 (1956)
Phys Abs 7690 (1955)
Khalatnikov2 I.M. see Abrikosov; Gortkov� L., P..; and Landau, L.D.
- A66 -
2-0E-03=4-14eir-USE-ONDr
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Khalfin,
"Causality Conditions and Physical Realizability Criterion in Quantuli
Field Theory," LAN 111, 345 (1956).
Phys Abs 3948 (1957)
pproved for Release: 2022/03/16 C06927295
1Q13_01W-Iglotartin�ONLY-
Kblebnikov� A.K. see Berestetskiy.
Khokhlov, Yu. K.
"Description of the Interaction of a System of Particles with the
Electromagnetic Field," ZhETF 26,576 (1954).
MR 1.6, 547 (1955)
NSA-6809 (1955)
Phys Abs 55(1955)
Khristov, Kb. Ya.
'Approximate Expression for Green Function in the Neutron Kinetic
Equation," DAN 1110 1197 (1956).
Phys Abs 5056 (1957)
Kirzhnits, D.A.
"Contribution to Field Theory Involving a Cut-off Factor," ZhETF
534 (1957)
JETP 2� no 3 445 (1957)
NSA 12, no 6 (1958)
"The Mass of Photon in Quantum Electrodynamics," ZhETF 30, 796 (1956).
Phys Abs 7125 (1956)
JETP 3, no 5 (1956)
"Mass Renormalization in the Tamm-Dancoff Method," ZhETF E5 971
(1956).
Phys Abs 7977 (1956)
JETP 3, no 5 (1956)
A: B=6; no 1,-204 (1957)
"On the Question of Meson-Nucleon Interactions," ZhETF 27, 6 (1954).
MR 17, 1166 (1956)
Phys Abs 57 (1955)
Klepikov, N.P.
"Application of the Theory of Singular Integral Equations to Problems
of Scattering of Particles in an External Field," ZhETF 30,
701 (1956), sup to E5 no 415.
MR 18, 259 (1957)
Phys Abs 8002 (1956)
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2.01-01=-14th-usr-orror
1.1111111111111111111111"111111.77�""ecl for Release: 2022/03/16 C06927295
Kli
14
Approved for Release: 2022/03/16 C06927295
aga--QUICIA43-ii6E-OITLY-
Wantum
;he
ic
23,
(1956).
'1
.954 ).
.oblems
"Radiation of Photons and Electron-positron Pairs in a Magnetic
Field," ZhETF 26, 19 (1956).
Phys Abs 10479j1956) -
"Solution of the System of Equations for a Vacuum Functional,"
DAN 100, 1057 (1955).
MR 17, no-2, 221 (1956)
Phys Abs 8489 (1955)
- -"On. the Theory of the Vacuum Functional," DAN 98, 937 (1954).
MR 16, 887 (1955)
Phys Abs 7990 (1956)
Klepikov, N.P. see Sokolov, A.A.
Klimontovich, Yu. L. (also Klimontovich, Yu. L.)
"Determination of Characteristic Values of Physical Quantities by
Means of Quantum Distribution Function," DAN 108, 1033 (1956)
MR 18, 360 (1957)
A: -1425
"Relativistic Equation for the Quantum Distribution Function,"
DAN 117., 927 (1952).
MR 14, 826 (1953)
NSA 3970 (1953)
Phys Abs 3135 (1954)
"Second Quantization in Phase Space," DAN 96, 43 (1954).
MR 16, 888 (1955)
Phys Abs 8571 (1956)
"On the Method of "Secondary Quantization" in Phase Space,"
ZhETF 33, 982 (1957)
BSA 12, no 4 (1958)
and Silin,
"Spectrum of System of Interaction Particles," ZhETF 23, 151 (1952)
NSA 3291 (1953)
Kobozev, N.I.
"On Physical Interpretation of the Broglie Equations," ZhETF 29,
2007 (1955)
NSA 2759 (1956)
Kolesnikov, N.N.
"On Green's Function in Radiation Diffusion Relation," ZhETF 33
817 (1957).
NSA 12, no 4, (1958)
-A68-
1113,_DEEIC-TAirifJE-07drr
moved for Release: 2022/03/16 C06927295
11
Approved for Release: 2022/03/16 C06927295
_.E.OB�ORK-9-141frtist�OITLY-
Kolesnikov, N.N. see Ivanenko, D.
Kompaneyets, A. (See other spelling: Companeets, A.S.)
Korst, N. see Brodskii, A.
Krokhin, 0.N. see Berestetskiy, V.B.
Krolikowski, W. and Rzewski, J.
"On Potentials in the Theory of Quantized Fields," Nuovo Cim III,
260 (1956)
MR 225 no 2 (1958)
Kudryavtsev, V.S.
"Oa Quasi-classical Quantization," ZhETF 31, 688 (1956)
JETP 4, 527 (1957)
Phys Abs 2967 (1957)
A: 1735
KUni,
"Dispersion Relations for Nucleon-nucleon Scattering," DAN 111 571
(1956).
Phys Abs 5063 (1957)
Kunin, P. Ye.
and Taksar, I.M.
"On Relativistic Effects in the Interaction of Nucleons," Latv PSR
Zinat Akad Vestis no 8, 137 (1952).
Phys Abs 9952 (1954)
"Some Relativistic Properties of the Behavior of Spin 1/2 Particles,"
ZhETF 321 506 (1957)
JETP 51-426 (1957)
Kurdgelaidze, D.F.
"Non-linear Scattering in Electrodynamics and Mesodynamics," Vestnik
Moscow University 9, no 8, 81 (1954).
MR 17, no 1, 113 (1956)
"On the Non-linear Generalization of the Meson and Spinor Field
Equations," ZhETF 32, 1156 (1957)
JETP 2, 856 (1957)
Phys Abs 2149 (1958)
Kurdgelaidze, D.F. see Ivanenko� D.
- A69 -
JSJELDERICTAirliSE�ONEY�,
".�
11111111111111111.111111111111111.--
Anoroved for Release: 2022/03/16 C06927295�
571
?SR
"
stnik
Approved for Release: 2022/03/16 C06927295
122L0EncrEkb-11Sr-DICY-
EUrtenkov,
"Statistical- Treatment of Elementary Particles Structure," ZhETF 33
554 (1957)
JETP 6,.'433.(1958)
Phys Abs 3712 (1958)
Landau, L.D.
"On the Quantum Theory of Fields," Niels Bohr and the Development of
Physics, p 52-69
MR 17, 692 (1956)
"Gradiant Transformations of the Green's Functions of Charged Particles,
ZhETF .22) 89 (1955).
JETP 2, 6o (1956)
Phys Kips 8482 (1955)
"On the Multiple Production of Particles during Collision of Fast
Particles," IAN 17, 51 (1953)
NSA 5195 (1955)
and PomerancUk, I.
"On Point Interaction.in,Quantum Electrodynamics," DAN 1020 489 (1955).
MR 17, 440 (1956)
NSA 5830 (1956)
and:Abrikosov, A. and ghalatnikov, 144. -
"An Asymptotic Expression for the Ureen.FUnction;of a Photon in Quantum
ElectrodynRmics," DAN 22, 1177 (1954).
.,MR, 16, 316(1955). -
NSA-4808 -(1954). -
Phys Abs 7968 (1956)
"An Asymptotic Expression for the Green Function of an Electron in
:Quantum Electrodynamics," DAN 22,. 733-0:954).
Det_16,i 316(19551
Phys Abs 7967 (1956) and 1049 (1957)
"The Mss of Electron in Quantum Electrodynamics," DAN 261
(1954). . �
MR 16,-316 (1955)
Phys Abs 7969 (1956)
"On the Quantum Theory of Fields," Nuovo Cim III, sup 80 (1956)
MR 18, 97 (1957)
"On the Removal of Infinities in Quantum Electrodynamics)" DAN 95,
497 (1954). ,
MR 16, 315 (1955)
NSA-4466 (1954)
Phys Abs 7966 (1956)
- A70 -
I_Igt--CaraCZAkrifeE-OXLI-
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pproved for Release: 2022/03/16 C06927295
_EDa_canoTAL-tisz-cgra-
Landau, L.D. see Belenki, S.S.
Lapidus, L.I.
"Isotopic Invariance and Creation of Particles," JETP 740119
NSA 12, no 4 (1958)
"Application of Dispersion Relations to 7r-N Scattering at .E;:
ti.oint.Institutefor-Nublear Research (preprint)
A: P-113 (1958)
Lapidus, L.I. see Galinin A.D.
Larin, S. see Ivanenko, D.
Lebebev, V.I. see Ivanenko, D.
Lipmanov, E.M.
"On Invariant Commutation Relations and the Exclusion of Supplement
Conditions in Quantum Theory of the Meson Field," DAN 67,
627 (1949).
� "Radiative Corrections in the Decay offi-Mesons," DAN 22, 999..(1953
NSF-tr-139 (English translation)
Phys Abs 3081 (1954)
"Regularized Theory of Systems of Fields," ZhETF .32, 214 (1956).
nays Abs 5679 (1956) -
"A Relativistically Invariant Form of Electrodynamics without Longi-
tudinal and Scalar Fields," ZhETF 27, 135 (1954).
MR 16, 318 (1955)
Phys Abs 721 (1955)
"Relativistically. Invariant Formulation of Electrodynamics without
Longitudinal and Scalar Fields," ZhETF 30, 538 (1956).
MR 18, 174 (1957)
Phys Abs 6343 (1956)
"Quantum Theory of Meson Field," DAN 627 (1949)
Liubimov, A.L. see Zartavenko, L.G.
Livshits, M. S.
'1-The Application of Non Self-Adjoint Operators to Scattering Theory,"
JETP 3, 91 1957)
A71 -
22:LIZEIGIAT2-155t-Orrr
Approved for Release: 2022/03/16 C06927295
nor
ov
7)
ergies41
ritary
53).
Approved for Release: 2022/03/16 C06927295
_ECE-012447.Par-usE-mrr
"On the Compound State Formed in the Scattering of Elementary
Particles," DAN 3, 799 (1950:.
.Phys Abs 5849 (1957).
"Concerning the Application of,Npn:Self..adjoint Operators in Scattering
Theory," ZhETF 31, 121 (1956).
Phys Abs 1071 (1957)
"The Scattering Matrix of the Compound System," DAN 3, 67 (1956)
Phys Abs 3961 (1957)
Logunov, A.A.
"Concerning a Certain Generalization of the Renormalization Group,"
ZbETF 30, 793 (1956).
Phys Abs 83 (1957)
JET? 766 (1956)
"Dispersion Relations for Virtual Processes," DAN 117, 792 (1957)
Phys Abs 724 (1958)
"Green's Function in Scalar Electrodynamics in the Region of Small
Momenta," ZbETF 29, 871 (1955).
Phys Abs 2643 (1956)
JET? 2, no 2 (1956)
"Spectral Representation and the Renormalization Group," DAN 109,
740 (1956).
Soviet Physics Doklady 1, 478 (1956)
NSA 2203 (1957)
Phys Abs 1051 (1957)
MR 19, no 1 (1958)
A: �1436
"Vertex Part in Scalar Electrodynamics in the Region of Large Momenta,"
DAN 106, 223 (1956).
Soviet Physics Doklady 1, 420 (1956)
MR 17, 1033 (1956)
Phys Abs '7124 (1956)
and Stepanov, B.M;
"Dispersion Relations for the Photoproduction of Pions," DAN 110,
368 (1956)
Soviet Physics Doklady 1, 552 (1956)
and Tavkelioze, A.N.
"Dispersion Relations for Photoproduction of Pions of Nucleons,"
ZhETF 32, 1393 (1957)
JET? 5, no 6 (1957)
-A72-
IgLOELICIPeireat�ONLT
Anninved for Release: 2022/03/16 006927295
pproved for Release: 2022/03/16 006927295
-riClit-441P-10-1:AL�t1Sr-OBIST
and'26Vkelibie$A:.14.-and.Solovyov;
"Photoproduction Processes and Dispersion Relations," Joint 'Institute
of Nuclear Research,. Laboratory of Theoretical Physics, Dubna$
USSR Moscow State University, USSR (1957)
AIudIehrThisits 44.427(1957)
Logunov, A.A.; Solovev, L.D.; Kukin, V.) Frenkin,.A.R.
"Dispersion Relations for Virtual Photoproduction,"
ReSeardhi.
A: P-161 (1958) (Preprint)
Logunov, A.A. see BogolyUbov� N.N.
Lokhov, Iu. N. see Galanin� A.G.
Lomsadze, Yu.M.
"A Possibility in the Quantum Theory of Fields," ZhETF 31, 887
Phys Abs 3958 (1957)
A: 1787
"Concerning a Certain Possibility in Quantum Field Theory," JETP 11.0
754 (1957)
NSA 12, no 4 (1958)
".-poti the' Potential in the Pair Theory Of Nuclear Forces." DAN 11D,
545 (1956).
Phys Abs 1905 (1957)
A: 1646
MR 19, no 1 (1958)
Soviet Physics Doklady 1, 571 (1956).
"On the Singularity of the Electromagnetic Potential in Ust Higher
Approximations of Perturbation Theory,." ZhETF 22�:707 (1956).
Ref. Zhur Fizika$ no 2 (1957), no 2946
A: i3-5
Nhksimenko, V.N.
"On Annihilation of Nucleons." ZhETF 33 232 (1957)
JETP 6, 189 (1958)
Markov, M.
!onDynamically Deformable Form Factors in the Theory of Elementary
Particles,"
Nuovo Cim v III, sup 760 (1956)
A73- ,
-F-OR-013455EL-ONL-T-
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Matve
Matv
Med.'
ate
e for
Approved for Release: 2022/03/16 C06927295
-F4R�Q171=F-17eV#L-711$11"-ONLY
"On Dynamically Deformable Form Factors in the,Theory of Elementary
Particles."
Supplemental Nuovo Cliii, v a, no 2 ,(1956)
"A Dynamically Deformable Form Factor of Elementary Particles,"
ZhETF ?..2, 527 (1953).
Phys Abs 733 (1955)
"On the Theory of the Dynamically Deformable Form Factor," DAN 101,
51 (1955).
MR 1p no 1, 113 (1956)
Phys Abs 7992 (1956)
Mhtveyev, A.N. (also Matveyev)
"Operational Method in Quantum Field Theory," Vestnik MOSCOW
University, no 8 (10), 99-104 (1953)
"The Role of Spin in the Radiation from a Radiating Electron,"
. ZhETF 2., 479 (1956).
JETp.4;409 (1957)
"The Role of Spin in the Study of the Radiating Electron," ZhETF 22,
700 (1955)
JETP 2, 356 (1956)
Matveyev, A.N. see Sokolov0.A. .
Ma ea-, ICE. and Shirkov, D.V.
"On Thirring's Two-dimens4nal Model," Joint Institute for Nuclear
Researqh, Laboratory of Theoretical Physics
A: P-187 (1958) (Preprint)
Medvedev, B.V.
"On Construction of the Scattering Matrix I. Integral Causality
Condition in Bogolyubov's Method," ZhETF 31, 791 (1956).
Phys Abs 3006 (1957)
JETP 4, 671 (1957)
NSA 12, no 4 (1958)
"On Construction of the Scattering Matrix II. Non-local Interaction
Theory," ZhETF 12., 97 (1957)
JETP 6, 343 (1958)
Phys Abs 5072 (1957)
"On the Construction of the Scattering Matrix in Quantum Field Theory
with non-local Interaction," DAN 1030 37 (1955).
MR 17, 443 (1956)
NSA-6813 (1955)
A711- -
_Ecal-ornGloarem-erzr
Annroved for Release: 2022/03/16 C06927295
p�roved for Release: 2022/03/16 C06927295
'4014-GPIfferakt-IISE-ONET
'."On,theTnitarity-:of the'S-matrixin the-Quantum Theory 'of aliad
the Non-local Interaction," DAW 100, 433 (1955).*
MR 17-, 565 (1956)-
Phys Abs 6755 (1955)
NSA- 299541955) , '
aad-Bonch-Bruyevich�
"Invariant Construction of Quantum Field Theory," ZhETF 210 425
(1952)..
and Polivanov� M.K.
"On a Classical Model of Indefinite Metric," Joint Institute for
Nuclear Research
A: P-180 (1958) (Preprint)
Medvedev, B.V. see Averbakh; Bonch-Bruyevich, Bogolyubov, N.N.
Mickevic, N.V.
"The Scalar Field of a Stationary Nucleon in a Non-linear Theory,"
ZhETF 299 354 (1955)
MR 17,1031 (1956)
JETT' 2, 197 (1956)
Migdal, A.B.
"The Momentum Distribution of Interacting Fermi Particles,"
ZhETF 32, 399 (1957).
dEle 5; 333 (1957)
and Polievktov-Nikoladze,
"Quantum Kinetic Equation for Double Collisions," DAN 103, 233
(1955).
MR 18, 98 (1957)
MikhayloVI-V. see Baldin� A.
Minlos, R.A. see Gel'fand,
Mirianashvili,
"On the Relativistic Magnetic Moment of Charged Particles," Soobsceniya
,kadNauk.Gnizin. SSR.-8, 613- (1947).
MR 14, 339 (1953)
Niriannshvili, �M.M. see Ivanenko, D.
Natanzon,
"Self Acceleration of a Charge Under. the Action of its Own Field,"
ZhETF 25,..� 448 (1953).
NSA 1620 (1956)
- A75 -
.E013,-01eFIGEffe-11813-ONLY-
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pLLaHn`
Nova
in
Approved for Release: 2022/03/1
:201,0E,F=T:Par,igffE-Mity-
Neganovr!BA �
"The Problem of Nuclear Structure, ZhETF33 -60 (1,957)
JETP 6, 200 (1958)
7Tiq.StructureHofNucleont,.",JointInptitute of Nuclear Research,
Laboratory of Nuclear I'roblems(1957) 23 pp
NSA 12, no 2 (1958)
Benicia} N.F.
Quantnm,Theorycf a,"Radiating" E1ectronl" DAN 85, 1259 (1952).
MR-I40 437'(1953)
"Quantgm Theory.of a Radiating:Electron. II." ZhRTF 27,. 421 (1954).
16, 982 (1955)
NSA-I422 (1955)
Phys Abs 1909 (1955); Phys Abs 5521 (1953)
Novo0.110Y$T4.*Lieningrad,StateUniversity)-
t'Application of Fok's,Method of Functionalt to the Problem of Self-
Energy." ZhETF 22, 264 (1952).
MR 14, 228 (1953T-
.. ESA 1240 (1953)
"Causal Operator in Quantum Field Theory." DAN 22. 533 (1954).
MR 16, 546 (1955)
NSA 2093 (1955)
"On the Choice of the 'Unperturbed' Energy Operator in the Theory of
the Interaction of a Nucleon with the Pseudoscalar Keson Field."
DAN 92, 931 (1953). English Translation: NSF-tr-217
Phys Abs 8045 (1954)
"On Eigen-energy of the Electron and Radiative Corrections.
DAN 83, 201 (1952).
Phys Abs 5294 (1953)
"Quantum Field Theory with Causal Operators." ZhETF 31, 493
JETP 4, 553 (1957)
Phys Abs 1888 (1957)
A: 1620
"On the Quantum Theory of a Field with Causal Operators," DAN
723 (1954).
MR 16, 778 (1955)
NSA 2045 (1955)
Phys Abs 8572 (1956)
-A76-
22,
r,r,muRr1 for Release: 2022/03/16 C06927295m.0.0.------
pproved for Release: 2022/03/16 C06927295
zopr-eme-wi--tysz-onr
"Quantum.Theory.of a Field with Causal Operators and the: 8 hoogo
� *Functional," DAN 104,-47 (1955). �
922 (1956)
"SdaId'TtaneformatiOn'and.Virial Theorem in Quantum Field Theory,"
-MEW 31, 171 (1957). .
JETP 5,138 (1957)
Phys Abs 5890 (1957)
"Methods of Functionals in Quantum Field Theory," UFN 61, 3 (1957).
Phys Abs 6916 (1957)
"The Variational Principle and the Virial Theorem for the Continuous
Dirac Spectrum," ZhETF 31, 1084 (1956).
JET? 4, 928 (1957)
Ogiyevetskiy, V.I. (Electrophysical Laboratory Akademii Nauk USSR)
"On Possible Interpretation of Perturbation Series in the Quantum
Theory of Fields," DAN 108, 919:(1956),
NSA 2202 (1957)
"A Possible Interpretation of the Perturbation Theory Series in the
Quantum Theory of Fields," DAN 109, 919 (1956).
Phys Abs 1048 (1957) MR 18, 54171957)
Okun, L.B. and Pontecorvo, B.
"Some Remarks on Slow Processes of Transformation of Elementary
Particles," ZhETF 32, 1587 (1957)
MI' '5, no 6'(19577�
_
Ovsyannikov, L.V.
"General Solution of the Equations of the Renormalization Group,"
DAN 109, 1112 (1956).
Phys Abs 1893 (1957)
At 1627
MR 19, 120 (1958)
Parasyuk, 0.3.
"On the Theory of Causal Singular Functions," DAN 100, 643 (1955).
MR 17, 112 (1956)
Phys Abs 7957 (1956)
"Multiplication of Causal Functions for Non-coincident Arguments,"
IAN 20, 843 (1956).
MR 19, 250 (1958)
-A77-
zcs--onalsakfrea-enr
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Paras3
Pekar,
Pek
Pet
Pe
Pc
Approved for Release: 2022/03/16 C06927295
..� z0i?..44=r4eatiorteE7oprzr
OUS
he
If
Parasyuk, O.S. see Bogolyubov, N.N.
'
Tekar. S.I. (Physics Institute of Ukranian Academy of Science)
'Criteria of Applicabi141y,ofthe Theory of Strong Coupling of Particles
with a Meson Field," MEW 271 579'41954). MR 16, 1186 (1955)
NSA 1691 (1955) Flays Abs 1525 (1955)
"On the Existence of Stationary Quantum States of Point Nucleon Inter-
acting with a Meson Field,"�ZbETF 220 599 (1955). JETP 2, 462
,-(1956) ,;-MR 181 444:0.957):Phys Abs 1855,(1956)
"The Freely Moving Nucleon," ZhETF 411 (1956).
MR 16, 1186 (1955)
NSA 2091.(1955) .
� Phys_Abs,1524A1955):.
"Non-existence of Discrete Energy Levels and the Corresponding States
for Particle with'Spin_1/2,in,a Given PseudoscalarPotehtial
Field," DAN"/, 1011 (1954). MR 16, 983 (1955)
."Strong Coupling Nueleomesodynamics 1. Approximate Method- Spin.'-Charge
Motion," ZhETF 30, 304 (1956)k...sup to 30, no.2-16:(1956)
MR 18, 174 (195TT Phys Abs 4835 (1956) A: B-6
"Theory of Strong Coupling of a Particle (Nucleon) with a MeSon Field,"
ZhETF 21, 398 (1954).
JIR 16v11186,(1955)
N5A-1421:.(1955).
Phys Abs 1523 (1955)
Pekar, S.I. see Beyyer, V.N.; Buimistrov, V.M.; and Dykman,
Peterson,. V.R.
4fProblem of the Transverse: Energy of the Electron. in a Linear
Generalization of Electrodynamics,",ZbETF 24, 56 (1953).
Phys Abs 9937 (1954)
Petras, M.
"A Note to Bhabha's Equation for a Particle with Mass Spin 3/2,"
Czech J,Phys, 5, 418 (1955).
Phys Abs 1849 T1956)
Podgoretskiy, M.I.
"On Superpositions According to the Internal Structure of Elementary
Particles," ZhETF 331 790 (1957).
NSA 12., no 4 (1958T
-A78-
Emixengoareso-estir
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Pokrayskiy, V.L.
"Generalization of Gauge Invariance and Combined Inversion,
269(1957). Phys Abs-724 (1958)-
JETY,6-1 208 (1958) NBA 8895 (1958)
.7011--OFFIGEkL�USE-ONtr
and Rumer, Iu. B.
"Note on the Theorem of Pauli on the Relation of Spin and Statistics."'
zup-3, 264 (1957)
"Conservation of Parity in the: Theory of Elementary Particles," MEW
� 33, 277 (1957) �JETP 6, 208 (1958) Phys Abs 726 (1958)-
Poliyevktov-Nikoladze,
�On the Derivation of the Relativistic. Equations for Free Particles
with Spin 1/2," Soobsceniya Akad. NaUk Grzin. SSR 9, 11
� (1948). MR 14, 340 (1953)
-"On the Green's Function for a Photon," DAN 105, 703 (1955).
MR 11, 1260:(1956).
�"Renormalization Of Charge without Perturbation Theory," DAN 105,
:-458.(1955). MR 17, 1260 (1956)
Poliyevktov-Nikoladze N.M. See Migdal, A.B.
Polivanov�
"On a New Derivation of the Equations for Green's Functions in
Quantum Electrodynamics," DAN 100, 1061 (1955).
MR 17, no 1, 113 (1956)
Phys Abs 8490 (1955)
Polovin, R.V.
"Radiative Corrections to the Scattering of Electrons by Electrons.
� and Positrons," MEW 31, 14.4.9 (1956)
JETP 4; 385 (1957)
Polovin, R.V. See Akhiezer
Pomerancuk� I. Ya. (Pomeranchuk, I. Ya.)
"Equality of the Renormalized Charge in Quantum Electrodynamics,"
DAN 103, 1005 (1956).
MR 17565 (1956)
NSA 2949 (1956)
-A79-
2o3-olgrac,-Lkb-uar-eNtr
Porn
Pon
EEE
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 Approved for Release: 2022/03/16 C06927295
gaik-44Eneakb7e8rrany
"kGeneralization-of'Vord's(Ward's).TheoremEtOAhe:CaSe Of Light
Of Finite Wave Length for Particles-yith Spin:.-Zero," ZhETF 100,
41.11955Y.
mit Abs 9412 (1955)
"Solution of the Equations of Pseudoscalar Meson Theory with Pseudo-
less" scalar.Coupiing,"-ZhETF:29i-'869 (1955).'
Phys Abs 1061 (1957) _
14ar' "Vanishing of Renormalized Charge in Electrodynamics and .in Meson
Theory." Nuovo.Cim.III U86(1956)
:MR. 18, 540 ,(1957).
PhyClbs 6385 (1956)
"Oa Renormalization of Meson Charge in Pseudoscalar Theory with
Pseudoscalar Coupling," DAN 104, 51 (1955). �
MR11, 1033j1956)
'NSA-1,962:(.1956):.-
Phys Abs 1059 (1957)....
"On the Vanishing of the Renormalized Meson Charge in'Eteudoscalar
_Theory with Pseudoscalar Coupling," IMLN-2 461 (1955).
MR up 1034 (1956)
.1Ek2960,(1956)-::
Phys Abs 1060 (1957)
and Sudakov, V.V. and Ter-Marirosyan,
"Vanishing of Renormalized Charges in Field Theories with -Point Inter-
action." PlAys Rev 103, 784 (1956)
Phys Abs 7126 (1956
MR 18, no 6 (1957)
PomeraneUk, I. see Galanin
Tontecorvol B. (4.) see Okun'z L.
-lion-linearity. Of the Field in Conformal Rediprocity Theory."
JETP 5, 642 (1957)
NSA 12, no 8
Twachev, Ya. I. and Shirdkov� M.F.
� , 'Part Played by the Gravitational.FiellinAhe Formation of the Mass
of an Electron." 'METF�24)-375 (1953).
Phys Abs 9938 (1954)
2013-4AF-I-G-1442-W3E�ONtr
,,,,,m/pri for Release: 2022/03/16 C06927295_
pproved for Release: 2022/03/16 C06927295
� 417-I-GlAfk-USE7OTTEr
Rayski� G. (Institute of Theoretical Physics, Copernicus University,
,Toran0 Poland)
"Bi-local Field Theories and their Experimental Tests II " Nuovo
Cim 5, 872 (1957)
MR 14'1 no 2 (1958)
"Remarks on Bi-local Field Theory," ZhETF 31, 705 1956)
JETP 4, 577 (1957)
NSA 12, no 3 (1958)
Ryazonov, M.I. (Moscow Engineering - Physics Institute)
"Phenomenological Study of the Effect of Non-conducting Medium
in Quantum Electrodynamics," ZhETF 32, 1244 (1957)
JETP 5, 786 (1957)
Phys Abs 67(1958)
atus, V.I. (P.N. Lebedev Physical Institute Academy of Sciences, USSR)
hRenormalization of the Equations of the New Tamm-Dancoff Method,"
'ZhETF 300 965 (1956)
Phys Abs 7976 (1956)
JETP 50 820(1956)
"Invariant Representations of the Scattering Matrix," ZhETF 33 1264
� (1957).
JETP 6, 972 (1958)
"The Scattering- of Photons by Nucleons and Nuclear Isobarsl!"
JETP 3, 926 (1957) P.m
Rosental, I.L. (Lebedev Physics Institute)
"The Fermi Theory of Multiples Production of Particles in Nucleon
Collision," ZhETF 28, 118 (1955).
NSA 11.027 (1955)
and Tschernauski, D.S.
"Theoretische und Experinentelle Daten Uber die Erzeugung von
Tellchen bei Bohen Energien," UFN 52/ 185 (1954) .
Fort der Phys 4, 560 (1956)
Rudik, A. see Ioffe, B.L.
Rumer,.YU.,B. (Yenisei Teachers' Institute)
'Action as a Coordinate. pf,Space. IV0". ZhETF 21, 454 (1951) Se
RUM
Bull]
Rya
-A81-
1EFIGEA-IrteE ONLY-
Rz
Sa
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, 40,
Approved for Release: 2022/03/16 C06927295
las-ognefitb-usz-oNa-
"Action as a Space Coordinate," ZhETF 22, 742 (1952).
MR 14, 606 (1953)
Phys Abs 1362 (1953)
"Action ass. Space Coordinate VII," ZhETF _3) 35 (1952
MR 14, 706 (1953)
Phys Abs 2925 (1953)
"Action as Coordinate of Space VIII, IX," ZhETF 24, 303 (1953)
Phys Abs 33, 34 (1955)
Rimer, Yu. B. see Pokrovskii, V.L.
Ruusik, I.Kn. (Institute of Physics and Astronomy, Academy of Sciences)
"Notes on Electrodynamics with'Bigher Derivatives," ZhETF 27, 260
(1954).
3SR) Phys Abs 722 (1955)
It
Ryazanov,
"The Sum Over Trajectories for Dirac Equation," ZhETF 23, 1437
(1957)-
NSA 12, no 9 (1958)
Ryndin, B. (M.) and Smorordinskiy, Ya.A.
"Invariant Transformation Cross-section of Non-polarized Particles "
DAN 103, 169 (1955).
BSA 7205 (1956)
Rzewuskil J.
"Conservation Laws in Non-local Field Theories," Acts Phys-Po1'
'12) 14'(.953)
MR 16, 980 (1955)
"Quantization of a Certain Class of Non-local Field Theories," Acta.
Phys. Polon. 100 (1953)
MR 160'981 (1955)
"On Inversions of Space and Time." Acts Playa PO1 435.(1957)
Owuski� J. see Krolikowskil W.
lta.4lau_2111. see Shirokov, Yu.M.
AOldowitschl J.B.(see also Zeltdovich, J. B.)
ftUber die Theorie- der Antiteidchen,.die LachungenIder Elementarteilchen
.und dip Eigenchaltzen Schwerer Neutrales Masonen," UFN
377 (1956) .
Fort der Phys 5, 570 (1957).
-A82-
OR 0?FIOIALUSZ oNrr
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20.11_01er,4e,likt..uss.-13NVir
Shapiro, I.S. (also Sapiro)
"Expansion of Wave Functions in Irreducible Representations of the
Lorentz Group," DAN 106, 647 (1956).
Soviet Physics Doklady 1, 91 (1956)
NSA 8o68 (1956)
Phys Abs 5698 (1956)
"Symmetry Properties in the Theory of Elementary Particles and
Nuclear Processes," UFN 53, 7 (1954).
MR 160 321 (1955)
"On Transformation Laws for the Spinors Appearing as Solution of the
Dirac Equation," ZhETF 22, 524 (1952).
MR 14, 339 (1953)
NSA 1291 (1953)
"On Transformation Properties of Wave Functions of Particles with
Spin 1/2," 711RTF .2.2, 412 (1952).
MR 14, 1047 (1953)
NSA7.181 (1954)
"Decay in Particle with Zero Rest Mass," ZhETF 27, 393 (1954).
NSA 1420 (1955)
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Shirokov, M.F. see Cr= Kuang Chao and Pugachev, Ia. I.
Shirokov, Yu.M. (also Iu. Shirkov)
"On the Conditions of the Relativistic Invariance of the Quantum
Theory." DAN 111, 1223 (1956).
NSA 6170 (19571
Phys Abs 5878 (1957)
"On the Interaction of Particles of a New. Type of Spin 1/2 with an
External Field." DAN 99, 737 (1954).
NR 16, 982 (1955)
Phys Abs 7980 (1956)
"On a New Class of Relativistic Equations for Elementary Particles."
DAN 94, 857 (1954).
MR 15, 916 (1955)
NSA-4178 (1954)
Phys Abs 1923 (1957)
"Quantum Electrodynamics in Configuration Representation I."
ZhETF 24 14 (1953).
Phys Abs 9925 (1954)
-A83-
zoii--eiaPlef*L--tisz�orrr
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he
Approved for Release: 2022/03/16 CO6927295
OTA-L-11,E7ONLY-
"Quantum Electrodynamics in Configuration Space III. Interaction
of Electrons and Positrons with the Electromagnetic Field."
ZhETP 24, 135 (1953).
NSA 7192 (1954)
Phys Abs 9927 (1954)
"Quantum Electrodynamics in Configuration Representation." ZhETF 24,
129 (1953).
Phys Abs 9926 (1954)
"A Relativistic Theory of Free Particles with Three Dimensional
Extension." ZhETF 22,539 (1952).
MR 14, 437 (1953)
NSA-6601 (1954)
"On the Spin of Particles with Zero Rest Mass." ZhETF 23,78 (1952).
MR 14, 437 (1953)
NSA-01.33 (1953)
"On a Theory of Interaction of a Three-dimensional Extended Particle
with an External Field." ZhETF 24, 47 (1953).
Phys Abs 9931 (1954)
"A Group-Theoretical Consideration of the Basis of Relativistic
Quantum Mechanics. I - The General Properties of the
Inhomogeneous Lorentz Group." ZhETF 22, 861 (1957).
JETP 6, 664 (1958)
NSA 15, no 4 (1958)
"A Group-Theoretical Consideration of the Basis of Relativistic
Quantum Mechanics. II. Classification of the Irreducible ,
_ Representations of the Inhomogeneoue Lorentz Group."
ZhETF a., 1196 (1957),
JETP 6919 (1958)
"A Group-Theoretical Consideration of the Basis of Relativistic
!Quantum Mechanics III. Irreducible Representation of the
Classes p,6 and Coat* the Non-cObb1etely7reducible Representations
of the Inhomogeneous'Lorentz Group,"� ZhETF 33, 1208 (1957).
JETP 6, 929 (1958)
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mil-cvn-Gorb-usz-orrir
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 and Sannikov, P.G.
"On the PYoblem of Unquantized Relativistically Invariant Renormalized
Equations fdr a Three-Dimensional Extended Particle."
ZhETF 31, 313 (1956).
JETP 13 (1957)
NSA.14.760 (1957)
Phys Abs 94 (1957)
A: 1457
MR 19, no 1 (1958)
Shirokov, Yu.N. see Filimonov, G.F. and Tumanov, K.A.
V.D. (P.N. Lebedev Institute of Physics)
"On the Article 'On the Spectrum of Excited Systems of Many Particles'."
ZhETF 28, 749 (1955)
Phys Abs 8519 (1955)
"On a Modified Tamm Method." ZhETF 21, 754 (1954).
MR 16, 778 (1955)
Phys Abs 6750(1955)
"On a Theory of Interaction of Nucleons and Mesons." ZhETF 24, 389
(1953).
NSA 208 (1955)
Phys Abs 49�(i95.5)
and Fainb erg, V. Ya.
"The Tamm-Dancoff Method." UFN 26.., 569 (1955).
Phys Abs 2657 (1956)
and Tam, I.E. and Fainberg, V.Ya.
"Method of TYuncated Field Equations and its Application to the
Scattering of Mesons by Nucleons." ZhETF 29, 6 (1955).
JEW 2, 3 (1956)
Phys Abs 8502 (1955)
Sirkov, �D.V.
"The Two-charge Renormalization Group in Pseudoscalar Meson Theory."
DAN 105, 972 (1955).
MR 17,1033 (1956)
Phys Abs 1065 (1957)
Skobelkin, V.I.
"On Double Ray-refraction in Non-linear Electrodynamics." ZhETF 27,
677 (1954)
MR 16, 547 (1955)
-A85-
Smoc
Smot
Sok(
Sok(
Sok!
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,-E9P791T:Ef'4-118E-01'cr
lzed
BmoorodinAk% ," � ,t ;:', ",,
"The Non-analYticitii-of'tfie Non-relativistic Scs4er.i.iliTAmiiitude
and the Potential." Joint Institutq Of NUile4i,Resparch
P-135 (1958) (Preprint)
SmosordinskiY, -
$
Sdkolik, GA;
"plassi4cat4,on of, Nort4421W-.Equatl.ons and Relativistl.cally
Envarian Interactions-b4RePreseniaions.Of-the_Lorentz
Group, and the Fusion Thedtr.."�DAN'106429j1956):,-
Soviet Physics Doklady 1, 57 (1956)
MR, 1031 (1956)
Joiv .81.7.967,(1956)
"Phys Abii-7116'(1956)
"On the Theory of Non-linear Relativisticialy Invariant Equations."
DAN la� 817 (1955).
11R 11.9. 331 (196)
Pbyp-A4.714.5,1195,6Y,
Sokolik, G.A. see Ivanenko, D.
Sokolov, A.A.
_"The Classical,Theory,:qp.,ElemeljOaT4rtiqlWNae:Poin-Elec74ron .
Veatnik MoSc64.0nliere*0-igsue. 2, 3:61 7) -
,
�
"On Relativistic Motion of Electrons in Ma0etio,Fields.vhen Quantum
Effects are Taken into Account." Mbsco4:4ate-University,
NUOVO CiM. III, Sup 743 (1956)
"Remarks onj4r-Quantum,ThePrY.4 p. raYioualFieid-;:"T,NeOnik
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9 (1952). �
MR 15, 82 (1954)
"FPrthar.Dlscusa0.011. t4P-guantOk:Ttledry*Radia4ng. Electron."
f -2943�
A: B-5
and Ivanenko, D.
"Quantum Field Theory." DAN 91, 47,(1953),
-
.and Kerimov, B.K.
On the "Damping Theoiy of Particle Scattering by a Fixed Center."
ZhETF 31, 1080 (1956)
JETP4 1 (197)
-
. e
0. A86 -
.49649.1Fr1714PLTUE�Nti
e 4 Sp A
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4014--AFFEelkL-17SEP-ONLY-
"Scattering of Zero Spin Particles Including Damp
611 (1956). '
MR 18, 443 (1957)
Phys Abs 8583 (1956)
"On the Scattering of Particles by it Form Center According to' tile-
Radiation Damping Theory." BUovo Cimento V, 783 (195T)'
"On the Theory of Scattering of Dirac Particles, Taking Damping into
' Account.' DAN 1050961 (1955).
MR 181 98 (19577--
Phys Abs 1064 (1957)
"Effect of Damping on Polarization of Dirac Particles." ZhETF 33,
827 (1957).
JETP 6, 639 (1958)
and Terpov, I.M.
"Motion of Fast Electrons in a Magnetic Field." DAN 2E, 537 (1953).
English translation, U.S. National ScienCe Foundation.
NSF-tr-137
Phys Abs 6272 (1954)
and Tystovich, V.N.
"Theory Of Electron Field Mass in the Presence of a Medium." zaw
301 136 (1956)..
Phys Abs 4820 (1956)
jETP .21y.94 (1956)
.NR 12i- 362j1958)
and Tumanov,
-"UndertaintY Relation and Fluctuation Theory.." ZhETF 395. 8p2
(1956).
Phys Abs 7123 (1956)
and Ivanenko, D.D.; and Ternov,
'"Excitation of Microscopic Oscillations by Quantum Fluctuations."
DAN 111, .334 (1956).
Phys Abs 3980 (1957)
MR 19, 362 (1958)
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"Damping Theory Study of Elastic. Scattering of Dirac Particles with
Account of Polarization Effects," Nuclear Physics .5y 390 (1958)
and Klepikov, N.P. and Ternov,
"On the Question of Rogation by. Fast Electrons in a;MOgnetic Field."
DAN 89, 665 (1953).
Phys Abs 9224 (1953)
A87 -
_ral-ornmfi-ust-orcr
_ � -
Soko:1
Solo'
Sao*
Solc
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nto
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2111=-03W-14-14artar-Olgrr
an&MatveeviAN. an&TernoviM.
"OmPaarization,:and'Spin-Fiffects,in the Theory of Radiating Electron,"
DAN ice, 65 (1955), . �
NSA 55g3 (1955)
Sokolov, S.N.
_1!Green!-S Function for a Photon Accurate to el4..." ZhETF 32 1261
(1957)-
Phys_Abs 722 (1958).
Solovyev, A.N. see Logunov
SOlovyev� .(Institute of-liuclearroblems)
'The Asymptotic Electron Greeep Function in the Infrared Region to
an Accuracy of e4." DAN 110, 203 (1956).'
Phys Abs 1895 (1957)
A: 1546
"Dispersion Relations for S and P Waves for:Mies-on Photoproduction in
First Order of VIM." ZhETF 33, 801 (1957).
JETP 6, 617 (1958)
Solovyev, VX.. (Institute of Nuclear Problems)
tuclear (Green) Propagation Function in Quadratic Approximation."
DAN 30 578 (1956).
Phys'Abs 3951 (1957)
"A Particular Model in Quantum Field Theory� AN 108;1041 (1956).
Soviet Physics Doklady 1, 392 (1956) -
MR 1.8, 444 (1957) .
-NsA705:(1957); 8888 (1958)
.1314.s.AbS 100 (1957) -
"Investigation of a Model in Quantum Field Theory." ZhETF 32, 1050
(1957)
JETP 5, 859 (1957)
Phys Abs 724 (1958)
NSA 6947 .(1958)
"On the Conservation of Combined Parity." ZhETF 33 537 (1957)
JET? 6, 419 (1958)
Phys Abs 2761 (1958)
:"The' Othe10:6- Of ConservatiOn.of'CoMbined parity Only in: Strong
. Electromagnetic and Weak Interaction8:".ftelear Physics 6,
618 (1958)
Phys Abs 2762 (1958)
A88
rspa_oigragulst-extr
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2011-OWIGEA:BIBE7ONET
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Stepanov,
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DAN 100- 939 (1955).
MR 11) 220 -(1956)
NSA-4029 (1955)
Phys Abs 7958-(1956) Su(
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Soviet Physics-Doklady 1, 346 (1956)
MR 18, 443 (1957)
NSA7506 (1957)
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Soviet Physics Doklady 1) 414 (1956).
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Sudakov, V.V. (Technical - Physical Institute Academy of Sciences)
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JETP 4, -.6i6 (1957)
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NSA 12, no 3 (1958)
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MR 19, no 1(1958)
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,
MR 17,1033 (1956) "
Phys Abs 11.809 (1956)
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Svi
Tak
Tak
Tal
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-...44..1141iTiff47:USTrOXEr
and Ter-44artirOsyan,X.Ai
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Phys Abs 3427 (1955)
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Tam, I. Ye. (P.N. Lebedev Physical Institute, Academy' of Sciences, USSR)
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*TRW 51:154-(1957) ,
Phys Abs 6885 (1957)
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NSA 7189 (1954)
Phys Abs 9941 (1954)
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pproved for
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Tam, I. Ye. see Ginsburg, V.L. and Silin V.P.
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A: 13-6
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(In Russian)
Phys Abs 2980 (1957)
"On a Rational System of Symbols for Fundamental Particles."
ZhETF 703 (1957).
,JET13-4,-574 (i957y,
Ter4fartirosyan, K.A. (Leningrad Physics - Technical Institute)
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Small." ZhETF 210 157 (1956). (In Russian)-
JETP II) 442 (1957)
Phys Abs 1054 (1957)
Ai. 1462
Ter-Martirosyan, K.A. see Dyatlov, I.I.; Pomerancuk, I.Ya.; and Sudakov, V.V.
Ternov, I.M. see Sokolov, A.A.
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Phys Abs 7120 (1956)
A: B-5
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_Eati-amaczitartme-en-r
Ts(
Ts(
Tsz
Tu:
Tw
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� YSELCALIGIArtl'afrONLY-
"Two-Electron-.Green's FunctUm in the Blo k-Nordsieck ApProximation."
:ZbETF 32, 1573.(1957).
Phys Abs 6i, no 724
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A: P-158 (Preprint)
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ZbETF 24, 369 (1953).
Phys Abs 40 (1955)
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these Rev. 13, 412
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NSA-4.906 (1955)
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MR 15, 489 (1954)
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203-arneziaren-ony-
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_
,
UlegIa) 1. .(Joint Institute of Nuclear Research)
�-"AnomolOus'.Equationt for Spin 1/2 Particles" ZhETF 38, .473 (1957)
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Verle,
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Phyt-Abs 51(1955)
Vladimirov, V.S.
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of Nuclear Physics (1958) (Preprint)
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Phys Abs 3977 (1957)
JETP II) 925 (1957)
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zaiLagnakfrusz-owzr
Yapl
Zayt
mimmomosommilliL+m"'"
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ute
yalaakTATATT-1313E6-eNtr
Yappao..YnA. (Leningrad State-University). .
In Connection with the Article of V,I. Karpman nOn the Question of
a Connection Between the Method of Regularization and Theories
of Particles with Arbitrary qpin!';" Miff 28, 123 (1955)4
Phys Abs 3436 (1955)
"On a Connection Between Theories of Regularization and Theories of
Particles with Arbitrary Spin." DAN 86, 51 (1952).
MR 1.11.i 608 (1953)
Phys. Abs.:39182 (19514):
NSA 3971 (1953)
NSA 4456 (1954)
Zaytsev, G.A.
"Concrete Representation of States of Particles with Spin 1/2 in
Non-relativistic QuEwtum Mechanics .,ZhETF 25, 653 (1953).
MR 17, no 35.330 (1956) '
Phys Abs 2410 (1955)
"Description of the Electromagnetic Field by Means
ZhETF 28.0 524 (1955).
JETP 13-4'(1955)
NSA 6090,(1956)
"On the Interpretation of Dirac's Equations for an Electron."
,ZhETF 29, 176 (is).
MR 17, no 3 (1956)
NSA 7599 (1955)
Phys Abs 68 (1956)
"Real Spinors in Curvilinear Coordinates and in Pseudoriemannian
Space." ZhETF 291, 345 (1955).
JETP 2, (1956)
MR 177 564 (1956); 415 94 (1957)
PhyT-Abs 6357 (1956J�
"Real Spinors in Four-dimensional Minkowski Space." ZhETF
667 (1953)
MR 1/, no 3, 330 (1956)
Phys Abs 2411 (1955)
of Matrices."
"Relativistically Invariant Equations for an Electron which Relanne
Dirac's Systems of Equations." ZhETF 28!, 530 (1955).
MR 12, no 3, 330 (1956) .
Phys Abs 2411 (1955)
-A94-
WflT C'FAL US ON
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X1474?.=,,OPELIelltrtISB-oNrr
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.,d66 (1955) Reviewed in NR .17) 330 '
clETP 21 240 (1956)
-NR. 18- 94 (195:
"The Use of Real Spinors for the Description of the Electromagnetic
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Phys Abs 4364 (1.955)'
"On the Fundamental Relativist ically Invatiant.Equation-fOr a Spin
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NSA 10373 (1957)
Soviet Physics Doklady 2, no 2 (1957)
Phys Abs 8389 (1957)
.Zartavenkol:L.G.; Liubimov, A.L.;.Ogievitsky, V.I.; and.Podgoretsky, M4I.
"On a Possibility of K-meson Investigation." Joint Institute Of
Nuclear Research, USSR (1957).
Nuclear Physics 3, 549 (1957)
Zelidovich, Ia. B. (see also Seldowitsch)
"Perturbation Theory for the One-dimensional Quantum Mechanical
_Problem and the Lagrange Method." ZhETF 32, 1101 (1956)
JETP 4, 442 (1957)
"On the Theory of Elementary Particles." DAN 86, 505 (1952).
Phys Abs 3098 (1954)
Zharkov, G.F.
"Nucleon-nucleon Scattering According to the Theory of Damping."
,JETP 2, 55 (1956)
"On the MagnetiC Moment of the Neutrino." ZhETF 241 529 (1953).
NSA 2089 (1955)
Zyryanov� P.S. see Eleonskiy, V114.
-A95-
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A
Ac.
DA]
Fo:
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NS!
NST
Nuc
NIX
MR
Nuc
Thy
Thy
Phy
Ame
UFN
VAN
Fiz:
Rest
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The following abbreviations are used in the bibliography:
A
Acta Phys Pol
DAN
Fort der Phys
IAN
E. JETP
NPA,
NSA
NSF
Nuovo Cim
MLRA.
MR
Nuclear Physics Nuclear Physics
Physica Physica
Phys Abs Physics Abstracts
Plays Rev Physics Review
American Translation of DAN Soviet Physics Doklady
Abstracts from other sources*
Acta Physica Polonica
Doklady. Akademii Nauk (Reports of the
Academy of Sciences of the USSR)
Forts chritte der, Physik
Izvestiya Akademii Nauk SSSR (News
of the Academy of Sciences USSR)
American Translation of Zhurnal
Eksperimentalinoy i Teoreticheskoy
izii(ZbETF)
Nuclear Physics Abstracts
Nuclear Science Abstracts
National Science Foundation
/
Il'Nuovo Cimento
Monthly List of Russian Accessiond
(Library of Congress)'
UFN
VAN
Mathematical Reviews '
Uspekhi Fizicheskikh Nauk (Progress
of the Physical Sciences)
Vestnik Akademii Nauk, (Progress of
the Academy of Sciences, USSR)
*English translations of Soviet �physics abstract, ReferativnnYZbUr0417
Fizika, and other sources were supplied mainly by the U.S. Joint Publications
Research Service in New' York City. .
� - �
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REFERENCES FOR'APTENDICES-B ANDC
*APPENDIX B
Part I
Kramers, H. A. "Rapp0rt6 du 8e Conseil Solvay 1948," p 241, R. Stoops,
Brussels 1950.
2. Dyson, F. J. Physieal Review 75, 486 1949
3. Schweber, S.S.; Bethe, H.A.; and de Hoffman, F. "Mesons and Fields,
vol 1,"- Row Peterson, Evanston, Ill., 1955
4. Lee, T.D. Physical Review 22, 1329, 1954
5. Kallen, G; and Pauli W.K. Danskevidensk. Selskl, mat-fys. Medd.,
30, (7), 1955
6. Kallen� G. Daaski vidensk. Selsk., mat-fys. Medd. 27 (12), 1953
7. Kallen, G. Helv. phys. Acta. 21, 417, 1952
8. Lehmann, H. Nuov. Cim. 11, 342, 1954
9. Gell-Mann, M and Low, F.E., Phys. Rev. 2J, 1300, 1954
10. Bogolyubov, N.M. and Shirkov, D.V. Nuov. Cim. 3 845 ,1956
11. Landau, L.D.; Abrikosov, A.; and Hatatnikov, L. Nuov. . .Cim. (Supp.)
3, 80, 1956
12. Schwinger, J. Proc. N.A.S. of U.S. 37, 452, 455, 1951
13. Fradkin, E.S., Soviet Physics JETP 2, 148, 1956
14. Pomeranchuk, I.; Sudskov, V.V.; and Ter-Martirosyan, K.A.; Phys. Rev.
103, 784, 1956
15. Abrikosov, A.A., et. al., Phys. Rev. 112, 321, 1958
16, Dyson, F.J. unpublished lecture notes, Comunbia U., spring 1957
17. Kallen, G., CERN Symposium, 1956, MN, Geheyag_Swit;erland, I
p 187, 1956
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Part II
1. Pomoranehtk, I. Nuovo Cim v3, p 1186, 1956
2. Lehmann, H.; Sytaniik, K.; and Zimmerman, W.Z.; Ii Nuovo Cimento,
v 2, p 425, 1955
opal
� APPENDIX C
Part I
1. Bogolytbov, N.N., Ukr. Mat. Zhurn. ?) 3, 1950
2. Bardeen, Cooper, and Schrieffer, Physical Review, 19.08L, 1175, 1957
3. Bogo1ydbov, N.N., Ii Nuovo Cimento 7, 794 1958
4. University of Maryland, Physics Deiartment, Technical Report 115
Part II
1. Physical Review, 104, 1760, 1956
2. 1 95, 1612, 1954
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