SCIENTIFIC ABSTRACT SHIRKOV, D.V. - SHIRMAMEDOV, M.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001549520013-1
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: August 23, 2000
• Sequence Number: 13
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

56-7-W66
A Note Concerning the Group of the Multiplicative
Renormalization in the Quantum Theory of the Field.
ASSOCIATION:
PRESENTED BY:
SUBMITTED:
AVAILABLE:
the gradient invarianoe in quantum electrodynamios), then
some of the constants occurring in the above mentioned
four relations can be in connection with each other. The
r,~normalization group, in fact, expresses a peculiar
"automodel-like" behavior of SCHWINGERIS equations.
Analogous contemplations can be carried out also in
theories with other interaction LAGRANGIANS.
(No Illustrations)
Moscow State University.
(Moskovskiy gosudarstvannyy universitet.- Russian)
-
11-1. 1957
Library of Congress.
CARD 3/3

_151 k'0 K.
AUTHOR DOGOLYU130 1N.,N,. _'embF~r of Jv- `1TR,'r,0W '-,,.V, YA. - 31~33_:-
101 N-arleonq
T I-, LE Dlsper3inn AelatJorj For tni rC61,
01~3persionnrje noc,,-noshenlya dlya K.-aptoi,ovikogo rasseyaniya na iruklo-
nakh -Ausoian)
P&MODICAL Doklady ~Akade=. Naux Milt, 1957,Vol 1.), Ur 3, PIP 529-532
Re?7eived 6/i~57 Reviewed 7/1957
AB ti -A RZ, T For the anadly3iS of the amplitude f cf 11,0-'IKON scattering tne authors con-
fine themselves to the examination if the ma4n term proportiona:1 t e
Toc-y toerefor-e put e - 0 in tne expretisions for the cor.responding varl-
at'lon d,3rival.ions, on w'aich only :strong Intgracticna are taken
tr, ac..-onnt~ 7"he'd-ispersion relatiorz f(,^ thri sca*tering of phc-~ons by nus-
be "1f1tr?r_-.ined by tn,~- zar.~- method by wbick N.14.130GO-TYU1,10V deter..
_nnd thf) d1spersion relati~=, for the scatterini of plon3 by nuc-locns.
At fi_rst an ansatz for -the amplitude of COMPSON scattering Is Written 1,own.
A functlrn on-curr.4-ni; in this an3atz i~ the impulse image of the ,causal"
matrix element. besides, "retardedv and "ad iced" matrix element3 are In-
trcdu:~ed. For the imaginary case,;~' - to . P~r_T,,,< functlor-5 S + T
s-,P_rt be defint~d which are analytical (with the exception.of lntersectic7
lines and poles on the real axis) within the entire plare of the comp2ex
v.)_-1RNe!5 E. The intersecticn lines and poles are determined accordlLg to
a complete functicn system by development of the PAUTMONUH of the meson-
:~na tne nucleon fieLd. The emplitude of COMPTON scattering In tafinity Is
assumed to have a pole of, at the mo3t, first order.

Di:jperniorz Relations For the GUMN zicat~ering on Nur-!-~,ons, PA, 313h
ex,-,"uqion of thr. unouservabl(~ domain of the negative enorgios is
The dispersion r,-lallions obta!ned herehave the fcllo-
wirg iniportant properties: Not only on the cccaslm of 1r. a
f lry;Fml directi~)n, but also for a lrterviLl. of reroil in;~se these
rplaticns contain no -anobsfr-ra~,.1,~ cf 4-nergy,
tl -, U3 t7 'a t-,cn)
.6'-- 0Ci'Al I ON Uniti~d Institute for Wclear Re-search
Bi
AV *-. 1 L t, Library c-I Congres-z:
C :Lr-j 2,11,4,

B-00-OLYLMOV, - Ili k-0 liyllio-layev i ch TOLLKAGHEV. Vladimir- Veniaminovich-,
_Y:Rsill evich; GUROV, X.P., red.izd-va; POLENOVI.
_2LPKQY.,D<xjy,
T.P., takhn.red.
blev method in the theory of superconductivity] Novyi metod v teorii
averkhprovQdimosti. Moskva, Izd-voAkad.naukSSSR, 1958. 127P.
(superconductivity) (MIRA 11:6)

BOGOLTUBOV. Nikolay Ilikoleyevich, HEDYEDIT, Boris Talentinovich, POLIVANDY,
Mikhail Konstaatinovich,; SHIRKOY, D.V. red.; TUMARKINA, S.A.,tekho. red.
[Problems in the theory of dispersion relations) Yoprosy teorii
disparsionnykh soatnoshanii. Koskvs. Goo. izd-vo fiziko-matematichookoi
lit-ry, 1958. 202 p. (MIRA 11:11)
(field theory)

AUTHOR: Shirirov, D.V. 89 -1-4/18
TITLE: The "Synthetic Kernel"-Method Applied -.n the Case of Neutron
Diffusion in a Medium Containing Hydrogen (Metod sinteticheskogo
yadra dlya zadach diffuzii neytronov v vodorodsoderzhashchey
srede).
PERIODICAL: Physics and Thirlmotechniques of Reactors (Fi2ika i teplotekh-
nika rrzaktorov3) Supplement Nr I to Atomnaya energiya, 1958,
CugsR)
A33STRACT: The physical idea of the suggested method consists in the per-
turbance of the correlation between the deflection of neutrons
and their change of energy in the individual act of scattering
on a viedium containing hydrogen, in which case the approximated
static correlation for a large number of collisions is conserved.
In this manner it is possible to derive an Approximation-diffusion
equation for a medium containing hydrogen. The equation is similar
to Peyerl'B equation and is suited for the direct numerical com-
putation of concrete problems. In the following chapters the fol-
lo,nring problems are theoretically dealt with:
1.) The synthetic transformation of the indicatrix in elastic
Card 1/2 slowing-dovm.

The "Synthetic Kernel" -mUethod Applied in the Case of Neutron 8C -1-4/18
1
I Diffusion in a.Mediin Containing Hydrogen
1
2.) The generalized Peyerl's equation, which describes slowing-
down.
There are 3 references, 2 of which are Slavic.
AVAILABLE: Library of Congress
Card 2/2 1. Peyerl's equation 2. Neutrons-Scattering-Hathematica1 analysis

A.UTHORS- Ginzburg, I.F., and Shirkov,D.V. SOV/155-58-2-32/47
TITLE: Asymptotic Behavior-(;f-1f,--gher -Oreen Functions (Asimptoticheskoye
povedeniye vysshikh funktaly Grina)
?BR1O11C,kL% llauchuyye dLokla&y visshey shkol-7. Tiziko-matematiches)Liye nauvi,
1958, Nr 2, pp 143-151 (USSR)
kBSTRICT% The asymptotic 'behavior of higher Green's functions for large
values of the scalar impulse arguments, recently investigated
by Konuma and Umezawa [Ref 1_7, is treated by the authors with
the aid of the method of the group of renormalization[Ref 21394,51.
The ultraviolet impulse asymptotic of higher Green's functions
is determined in two steps. At first the Lie equations are
established and solved for the invariant charges which characterize
the given variant of the field theory. Then the Lie equation is
solved for the impulse asymptotic of the considered Green's
function. The method is suitable for the investigation of the
Green's functions of real physical scattering processes. The
authors thank V*L.Beresinakiy for the valuable discussion.
There are 3 figures, and 6 references, 3 of which are Soviet,
1 American, and 2 Italian.
ASSOCIATION:Obllyedinen.iKy institut yadernykh issledovaniy (United Institute
-Gard-l-/-Z of Nuclear esearch)

240) SOV/20-122-1-11/44
AUTHORS: Mayyer,!!. E., Shirkov, D. V.
TITLE., On thQ Two-Dimensional Model Developed by Thirring (0 dvukh-
mernoy modeli Tirringa)
PERIODICAL: Doklady Akademii nauk SSSR, 1958, Vol 122, Ur 1, pp 45-47
(USSR)
ABSTRACT: Accordin- to 'Zhirringr (Ref 1), the non-linear theory of the
spinor field with the Lagrangian of interaction
L(x) = g:T(x)o,+(x)~(x)0n+(x):
i~~ investigated in a two-dimensional space. Here (10 - I;
a1, 02, 153 denote the usual Pauli matrices of the second
rank, an! the summation in the above-,-liven Lagran-gian is.
n n 1 . 1 2 2 3 3
defined as follows: 0 x a X I - a )e c - Ll x 0 _ a x 6
The above-given Laprangian is the only combination that is
symmetric with respect to a transposition of two anticom-
(or) two The authors investi-
mutating operators q) and
gate that element of the S-matrix which corresponds to the
C~rd 1/4 ecattering of 2 ~-particies of zero mass; this element may

On.the Two-Dir.,.ensional Model Developed by Thirring SOV/2o-122-1-11/44
be written down in the form
S - (ig/4n 2) JZ~_.(pl) ~O(q) ~Y(ql) +6(p)6(pl + q1- p - q).
I-FaP,y6 (pl#qllpjq)d 2p1d2pd2 qfd 2q
where the function P obviously is antisymmetric and summa-
tion ia carried out with respect to the dummy (nemoy) indices.
In the second order of the perturbation theory, the follow-
ing expression is found for
n 12 PP.PX P + ~ abX
(,n X a ) in __ Z - y6 - C
ap 76 Q 2 n P 2
There is P = (p'- p)/2, (p + q)/2, and C denotes a constant
which contains an infrared divergence. This divergence may
be eliminated from the normalizing considerations for scat-
tering processes of real particles. 11oreover, the last given
expression does not contain ultraviolet divergences. The final
exF.-ression 'or ap,16 is given explicitly. The authors then
try to improve the approximation properties of this expression
Card 2/4 for Pap,,t6 according to the method of the renormalization

On 'the '1'wo-Dimenuional 111odel Developed by Thirring SOV/2o-122-1-11144
-roup. The renornalization group for this problem has the
same structure as the renornalization group for a certain
variant of the non-linear neson theory. The corresponding
functional equations are given explicitly. The function T
which figures in these equutions denotes an invariant charge,
and there is T (Xtg) - 1. The charge is not renormalized in
the linear (with respect to g) approximation. All things
considered, this is a consequence of the fact that there is
no ultraviolet divergence. The authors then deduce an im-
Proved expression for r for the scattering of 2 real
particles. In a certain degree, the formula deduced in this
way is exact in the limit of small g, and it is very similar
to a result of Thirring for th~linit case of small g - A.
The authors thank V. Ye. "hirring for very useful remarksp
and also 11. N. 3o.-olyubov and B. V. Hedvedev for discussions.
There are 4 references, 2 of which are Soviet.
ASSOCIATION: Obl'yedinennyy inotitut yadernykh is3ledovaniy (United Institute
of Nuclear Research); 1-.1,atematicheskiy institut im. V. A.
Steklova Alkademii nauk SSSR (Mathematical Institute imeni
Card 3/4 V. A. Steklov AS USSR)

--SHIRKffp D-.-- V-. -(Dubna)-
"Theoretical Investigations of Dispersion Relations."'
Nuclear
report ppsented at the Intl. Conference on Nigh Energy/Pbpice, Kiev, 15-25 July 1959.
(at the session on Theoretical Investigations)

24( 3 SOV/56-36-2-39/63
U T H 0 P Shirkov, D. V.
TITLE: On the Euliation of Compensation in the Theory of Super-
conductivity (0b uravnenii kompensatsii v teorii sverkh-
provodimosti)
PERIODICAL: Zhurnal eksperiientallnoy i teoreticheskoy fizzil-i, 1951),
Vol 36, !1r 2, pp 607 - 612 (TTC--'R)
ABSTRACT: The !iuthor deduces a connection between the matrix elenents
of the variation derivatives of the scattering matrix and
of the ener,3y operator. The energy characteristics of a
many-body system can be expressed by the total S-matrix
OD
S= S 00 T(exp i H )dt
-00 1- 1 int(t
CD
This -method is used as t"'Ie basis of the considerntions
discussed in this paper. The kernel ,Z(k,kl) of the integral
equation is expressed by the vacuum matrix elemerts of the
variation derivatives of S, i. e. by ordinary Green (Grin)
Card 1/13 functions. The explicit expressions for theoe Green functions

On the Equ-tion of Compensation in the Theory of SOV156-36-2-39163
Superconductivity
can be found according to the method of approximate second
quantization. The second part of the present paper deals with
the connection of S and It and or their variation derivativsk.,
(R denotes the ener- operator). Formulae of the diecunned
type can be found also for the commutators of the quantitiee
S,R with the operatorn of particle production and particle
annihilation nnd, t1herofore, n1so for the varintion derivatives
of 3 and R with respect to these operators. In the third part
of the present paper, the transformations of the kernel q of
the compensation equation are discussed. The kernel ~t can be
represented as a sum of two terms:
,4(k,kl) -qC(k,k')+~~ ph(k,kl). The fir-t term Zc corresponds
to pure Coulomb effects. The calculation of the expressions
for QC and Q ph are given step by step. The- author thanks
N. N. Bogolyubov and V. V. Tolmachev for useful discussions.
There are 5 references, 3 of which are Soviet
Ca~-d 2/3

On the Equation of Compensation in the Theory of S-011/c6-1~6-2-WE3
Superconductivity
ASSOCIATIOIN: IMatematicheskiy institut iT. V. A. Steklova AVademii nauk S"SR
(Matheiatical Inrtitutc.- imeni V. A. Steklov of the Acade-ly
of Sciences, US"R)
SUBMITTED: Se~tember 1, 1058
Card 3/13

-2A
I'M SOV/56-37-1-20/64
AUTHOR; Shirkov, D,, T,
TITLE: On the Consideration of Coulomb Effects in the Theory of
Superconductivity (K uchetu kulonovskikh effektov v teorii
sverkhprovodimosti)
PERIODICAL: Zhurnal eksperimentallnoy i teoreticheakay fiziki, 1959,
Vol 37, TIr 10), pp 179-186 (USSR)
ABSTRACT: The equation for the compensation of the dangerous electron
diagrams is put into a symmetric form by transition from the
energy operator to the S-matrix; it is expressed by an.ordinary
Green function. The first rart deals with the sy=etric equa-
tion of compensation. The equation for the compensation.of
the dangerous electron diagrams in the theory of supercon-
ductivity (according to formula (5-19) in the book by
N. 11. Bogo.1yubov, V. V. Tolmachev,and D. V. Shirkov) can be
represented in the form
2
R ei E (k) (t+t ')dtdt' - 'Ov
~