SCIENTIFIC ABSTRACT GRIGORYEV, V.I. - GRIGORYEV, V.,M.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000516820003-6
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: January 3, 2017
• Document Release Date: July 27, 2000
• Sequence Number: 3
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

P11967
Relation Between the Matrices of Various S/056/60/039/003/053/058/Xx
Transitions and Multiple Processes B006/BO70
that a large number of bosons are producedl all the bosons have about
the same energies. On these assumptions, the equation for the matrix
V(ON,22) is set up according to formula (2), and the solution obtained
is discussed. The authors thank Ye. L. Feynberg and D. S. Chernavskix
for valuable comments. There are 6 non-Soviet references.
ASSOCIATION: Moskovskiy gosudarstvennyy universitet (Moscow State
University)
SUBMITTED: April 18, 1960
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J1 Iulo
S/18 62/000/003/005/012
Bill 112
YB
AUTHORS: Vavilovo B. T., Verdiyevq I. A., Goncharoval N. G.,
Grigorlyevp V. I., Meledin, G. V.
I ITLE t Quantum field theoretical investiCation of multiple processes
P'ERIODICAL: Moscowo Univeraitet. Vestnik. Seriya III. Fizika,
astronomiya, no- 3, 1962, 46-59
EYT : Multiple production of n-mesons in n-N,y-N, N-11, and r-n collisions
is studied and the corresponding graphic renormalization equations are
given. The mathematical structure of the theory is similar to that of
the Tamm-Dankoy method. It differs only in that the.infinite system of
equations does not break off, but a solution being reached through a
reduction of the proPagation function and on other assumptions. Ptoceeding
from the Tomanaga-Schwinger equation
1 -0 U HWU
6o 0,0 '1
1 01 oj
where U U(ij,rim,kl)
Card 1/5 ca'a 01 ij,nm k1 16'a oj

.'J/188/62/000/003/005/012'
Quantum field theoretical... Bill/B112
(ij,nm,kl)
U is the transition matrix for a graph with i, n, k incowing,
and J, m, 1 outgoing boson, fermion and antifermion lines, respectively.
For U~'J;nm) it is established that
tog
03
If cp,)
d4z U (P.) P1 04) X
Nun 1-1 4.1
P. + P, - P4)], (4),
X Q11.RM) C.XP liz ( " - E N - Y.
4-1
f'jlrtm) is a coefficient function,for the individual collisions,
,rhere Q
Its determined from the graphs. This method offers the advantage that
summation does not necessitate all Graphs being written explicitly ai in
the perturbation theory. Since a closed solution is impossible, the
procedure is simi,lified by disregarding the production of nucleon-
antinucleon pairs in the intermediate and final states, disregarding
spin effects, and assuming low energy in the mesons produced. In
addition, scalar and pseudoscalar mesons with scalar interaction are
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r B111 112
,Uantwn f i old theoreti cal . . . %
studied. Following the determination of R (ij,nm) for the n-N, j-N
.collisions the probability n
W. n1 (2r)l S IPP -P*i jQ(1R.11)1,x
2EP 2k~j
'S
a (E-, + k., (P + ki)
is obtained by insertion into (4) where ptk i is a four-momentum of the
final particles. The integral in (8) is the "ceneralized phase integral"
which, for N-N and n-n collisions has similar shape. Its calculation is
illustrated for n-N collisions. For N-N collisions, similar considerations
as for n-N collisions, give
W '_ (gm) 2n n/2
( n.
n 2%A2
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nl(z-i) 2n-1
)112 (2n - 1)1
((n +
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quantum field theoretical... B111/B112
where z For n-n collisions the interaction Is brought about by a
m 4
nucleon-antinucleon pair (a term T being added in the intt~raction
Hamiltonian). If meson scattering only is considered, this influences the
multiplicity only slightly. The angular distribution tend.3 to higher
isotropy in the presence of meson interaction. For the angular distribu-
tion of relativistic mesons in N-N collisions dn(G),,, 1 and for the
dg 9in3~
energy distribution
M2 k 2 2 2 2
+ 1n k + t..
dk 2 4k 1,3 k)
Summary of the results for multiplicity:
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quantum field theoretical ...
nN-Af (g M (Z". z
3 1. 2m
n- X~4 9.1. ( M
4
Ell
21A
Ec Ec
21L 1-
2,,
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B111YBI12
No qualitative agreement could be found between the iormulas and the
experiment. There are 5 fiEures and 1 table.
ASSOCIATION: Kafedra elektrodinamiki i kvantovoy teorii (Department
of Electrodynamics and Quantum Theory)
SUB:.;ITTF,D: July 16, 1961
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GEUGORIYEV 11 1 - SIDOROV, N.A.
Determining the permissible internal presmire in casings.
Neft. khoz. 41 no.2:25-29 F 063. (MIRA 17: 8)

ACCESSION NR: AP40437" S/0188/64/000/004/0056/0061
AUTHOR: GrIgorlyev, Vo 1.
TITLE: Broadening and shift of energy levels
SOURCE: Moscow. Universitato Vestnik. SerlYa 3. Fizlka, astronomiya. no. 4. 19(A,
-61
56
TOPIC TAGS: energy level, perturbation, renormallzation, quantum theory*0- boson,
fermlon
ABSTRACT: The problem of the broadening and shift of energy levels of a system
I subjected to the Influence of perturbations has been considered In many papers.
In this article an attempt Is made to develop an approach suitable for the study
of processes with an arbitrary number of particles In the Intitial and final
states. There Is also a discussion of how the remormalization method can be used
for eliminating discrepancies. The conditions for determining the renormalization
constants are written In the form:
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ACCESSION NR: AP4043799
where V -.#'* 0, that Is, In the absence of an external field, where I > Is a single-
boson state vector and I > Is a single-fermlon state vector. Before writing ex-
press I ons f or the sh If t and broadeni n9 of energy I evel s the author cl tes
T'f V Jul W.C. [al.
(2)
whe re Yn is the full set of state vectors (with quantum numbers denoted by the
single letter n) In the absence of perturbation
.0. (3)
Using the orthonormal character of the system Vn It Is possible to write equations
for Cn
(4)
+ C. W., Col.
60 IN) fit) +
C., + (X) V~. ce
60
(A).
riCc,d,
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ACCESSION NA., AP4043799
with the Initial conditions
C. (d.1
C Is rewritten (when n A n) In the form
n
C. (01 101 C. 101.
(6)
Substituting this into (4) it is found that the formal (K /-cr7 has not yet been
found) solution has the form
(7)
of *gift
where x1 Is a point of four-dimensional space-time lying on the hypersurface d'. so
pent there will be the T product of the operators entering Into
that in the !x
ir(xl) and Kn C Is easy to relate to the S matrix. In actuality, since
7
n
S (Vogl T (001 (8)
.It Is easy to show that
and since In "scattering typeP prob Isms vrqv -Y"o

ACCESSION NR: AP40437"
C. lei V: S (0,V91 T,%.
This makes It possible to rewrite C. In a convenient form:
X') S to, eel V
_-,>. (10)
C801 exp