SCIENTIFIC ABSTRACT TAVKHELIDZE, A.N. - TAVRIZOV, V.M.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001755120017-2
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 99
• Document Creation Date: November 2, 2016
• Document Release Date: July 16, 2001
• Sequence Number: 17
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

On the Group of Renormalization in Problems With a SOV/155-58-2-37/47
Fixed Source of Muclons
a
ASSOCIATION:Obllyedir,.ennyy,institut yadernykh issledovaniy (United Institute
- of Nucleax Reeesmh)
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16(2),21,(7)
AUTHORS:
TITLE:
Logunov,A.A., and Tavkhelidze,A.F. SOV/155-58-3-32/37
Generalized Dispersion Relations (Obobshchennyye'A.-~sperz~,-,n--.yi-~
oootnoqheni3-a)
PERIODICAL: Nauchnyye dc;klady vysshey shkoly. Fiziko-matematichenkiye natik--i
1958t Nr 3, PP 178-185 (USSR)
ABSTRACT: The present paper continues the earlier investigations of the
authors f-Ref 1,2,3,4-7. The authors propose a method for
obtaining dispersion relations for the r6actions a+b--iva'+c+d.
At the beginning of the reaction there i 's a nucleon and a bosoY4
at the end there is a nucleon and two bosons. In contrary to
f-Ref 1v29394_7 the authors do not assume that the energies of c
and d are equal. The ratio of these energies is fixed as Polking-
horn has done. An explicit calculation is made for the double
Compton effect (S'+p-2r+p). The paper contains three paragraphs:
�1 Kinematics of the process, �2 Investigation of the anti-
Hermitean part of the amplitude of the process, �3 Dispersion
relations.
There are 6 references, 3 of which are Soviet, 1 American,
1 Italian, and I German.
ASSOCIATION:Obllyedinenny,y institut yadernykh issledovaniy Institute
of Nuclear Research)
SUBMITTED: April 4, 1955
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33
21(7),16(2),16(1)
AUTHORS: Loguno,r,A.A.,Bilenlkiy,S.M.,and SOV/155-58-3-33/37
Tavkhe:Lidze,A.M.
TITLE: On the Theory of Dispersion Relations for Cniplex Processes
(K teoxii dispersionnykh sootnosheniy dlya slozhnykh prctsessov)
PERIODICAL: Nauchntye doklady vysshey shkoly. Fiziko-matematicheskiye nauki,
1958, Nr 3, pp 186-195 (USSR)
ABSTRACT: The prosent paper contains the proof of the dispersion relations
for the process lr+p--),2g+p in the case when the non-observable
domain is missing. At first with the aid of the principle of
causat;'on (in the formulation of N.N.Bogolyubov f-Ref ~_7) the
lagging and the leading amplitudes of the process are constructed;
the fi:-st one is combined with the direct process, the second one
is com'oined with the recurrent process. These functions are
defined for real values of energy lying above the threshold of
the process. Then the functions. and ~a(, E) (compare
f-Re f 6
_7) are cons truct e r and lower halfp1ane E,
reepecl;ively, are analytic and'*Mch agree on an interval of the
real airis. These functions define a single function being
analytj4:c in the whole complex E-plane 'with the exception of
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On the Theory of Diapersion Relations for Complex SOV/155-58-3-33/37
Processes
certain cuts along the real axis. At the banks of the cuts the
E) and ~a(,,,) for 9-0 tend to the lagging and leading
amplitiide, respectivoly.. The dispersion relationa appear an
conclusions by the application of the Cauchy theorem to these
functions.
There are 6 references, 4 of which are Soviet, 1 Italian, and
1 American.
ASSOCIATION:Obllyedinennyy institut yadernykh issledovaniy k fpiht Institute
of Nuclear Research)
SUBMITTED: April 25, 1958
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21(l)
AUTHORSs Logunov, A.A.9 Tavkhelidze, A.N., SOV/155-58-5-21/37
Chernikov, N.A.
TITLEs On the (luestion of the Dispersion Relations for Reactions
With 'Va:riable Number of Particles
PERIODICAL% Nauchnyye doklady vysshey shkoly. Fiziko-matematicheskiye
naukill'958,Nr 5,PP 120-123 (USSR)
ABSTRACTs In Z-Ref 1 7 Logunov set up dispersion relations for processes
with variable number of particlee. In Z-Ref 2,3-7 the analytic
proporties of the amplitude were treated. The authors use the
results from Z-Ref 1,20 7 in order to give in the present
paper for reactions of tRe double Compton effect a further
extension of those dispersion cases for which the dispersion
relations do not contain the nonobservable energy range.
�. 1 Kinematics of the process e. 2 Dispersion relations.
The authors thank N.N. Bogolyubov, Academician for discussiont
There are 1 figure, and 3 Soviet references.
ASSOCIATION: Ob"yedinennyy institut yadernykh issledovaniy (United
Inetitirte for Nuclear Research)
SUBMITTED: March 257~ 1956
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LOGUNOV, A. A. and TKIKHFJADZE, A. N.
Joint Institute of Nuclear Research, Iaboratory of Theoretical Physics, Dubna, USSR.
"Some Problems &eountered in the Theory of the Dispersion Reiations."
Nuclear KUsics, v. 8, PP. 374-393. (1958) (North-Holland Publishing Co.,
Tmsterdam.)
Abstract: Dispersion relations are obtained for a reaction i1volving a variable number
Of particles (a fermian and boson prior to the reactions and a fermion and two
identical bosons aftex the reaction). Cases are indicated for wbich an unobservable
energy region is absent in the dispersion relations. A justification of the dispersion
relations in the absence of an unobervable energy region is presented for the particular
process y-t p --> -j-, p -

AUTHORS: Tavkhelidze, A. N., Fedyanin, V. K. 2o-119-4-17/6o
TITLE: Approximated Equations for the Amplitude of the Scattering
of Photons on Nucleons (Priblizhennyye uravneniya dlya am-
plitudy rasseyaniya fotonov na nuklonakh)
FERIODICAL: Doklady Akademii Nauk SSSR, 1958, Vol,~ 1199
Nr i,p pp~ 69o - 693 (USSR)
ABSTRACT: The study of the scattering of photons on nucleons is able to
supply important Clues as to the mesonic structure of the
nucleon. The present work determines approximated equations
for the physical amplitudes on the basis of the diapersion re-
latione for Comptott scattering. The first chapter deals with
the kinematic examination of the amplitude. First, an expression
is written down for the amplitude of the process resulting from
rela.tivistic invariance. From the conditions of relativistic
invaxiance and 1;radient invariance it is poosible to determine
the number of independent structures and to find an explicit
expression bereof - In a pseudoscalar meson field the number
of independent structures is lo. If the invariance of the ampli-
tudet with respect to reflection as regards time is taken into
Card 1/3 account, this number is reduced to 6. The authors here write

Approximated Equations for the Amplitude of the 2o-119-4-17/6o
Scattering of Photons on Nucleons
down explicit expressions for these 6 independent structures.
Next, some symmetry properties of the invariant functions are
-------Ietected.-Im-the---second...cha,-,)t.er dispersion rel-itions for the----
relativictic amplitudee;L~L are derived. This is, however, only
an intermediate stage, and in the next chapter the dispersion
relations for the physical amplitudes are derivod. In the last
cho.pter the unitarity condition 'is derived. The dispersion
relations derived here connect the Hermitian and the anti-Her-
mitian part of the amplitude of the reaction. The unitarity
condition written down in single-meson approximation makes
it possible to express the anti-Hermitian part of Compton
sco.ttering by the amplitudes of photoproduction. In conclusion,
the! authors thank N. N. Bogolyubov, Member, Academy of Sciences,
USSR, and A. A. Logunov for their valuable discussions and for
the constant interest they displayed in this work. There are
5 references, 3 of which are Soviet.
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Approximated Equations for the Amplitude of the 2o-119-4-17/6o
Scattering of Photons on Nucleons
ASSOCIATION: Ob"yedinennyy institut yadernykh issledovaniy (United Institute
of Nuclear Research)
PRESENTEP: November 2o, 1957, by N. N. Bogolyuboy, Member, Academy of
Sciences, USSR
SUBMITTED: No-vember 14, 1957
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AUTHOR'!: Logonov, I Tavkhclilze, A. 1 -C, -4 -- 14,"7
T IT L E 'Me Anal! tical -r ~"_rti~csof 7the of a I-roce!3s Tn-
-iolvine a Verlable ..'timber of Particles ,kriaEticheckiye _~voystva
U
;.IMT)Iitudy protstassa s peremennyin chislom chaztits)
PE'dIGMICAL: Dokl--dy Akademii rauk S-~"Rj loq, rol. 120, NX 4, pI)97,;)9-74?
Us S R
ABSTRACT: A. A. Lonanov in the course of un earlier paper investi:7ated
the disper--ion relations for rrorpsses involvirv: a variable
number oil particles. In the present instance the nethol de-
veloped by N. N. Bogolyubov (Ref 2) is used for the rurpose
of Provin.-, these r~.-lations for the cave in which tnere exists
no energj domain that cannot be observed. Firct the Fourier
representatiormof the retarded and of the advanced matrix
element of the double Compton effect are explicitly -.-.,ritten
down. The authors investigate the function T(-~~,
ret adv
T ( F, 'Q1, T (E, the cncr:-,y vpectrun of
which i_~i here iliurtr- *t 15~ -1 in form of n drawing. The
larity oil the funct'.on can be eliminated by
Card 1/2 selecting a n~uitablo polynomial given here. The further

. SOV,12o-120-4-1 4/67
The Analytical Proverties of the Amplitude of a Frocess Tnvolving a 7ariable
I
Number of FanrticleS
contents of this nurely mathematical paper is a detailed de-
scription of the various stages of the computation. The ex-
pression. found i.,, explicitly written down. In conclusion Vie
authors thank N. IN. Bogolyubov, 11,1eriber, "IS US)SR, for his
valuable discussion of th13 paper. 'P;iere are 3 figures and
2 reference-, 2 of which are Soviet.
-AS.;OCTATION: Ob"yedinennyy institut yadernykh ic.,:1edoven-4y (United Insti-
tute of Nuclear Reoearch)
PH , rNTED: February 17, 1958, by !I. Bogolyubov, ',Iember, ,,~cadFny of
Sciences, UO-SR
SUBMITTED: February 5, 11,158
1. Mathematics
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MISTVIRISHVILI, M.A.; TAVIOMOZZ, AoNo
Problem of back dispersion mlationso Soob.A.19 Gruz.SSR 23
no.2:149-156 Ag 159. (KIU 13:2)
1. Tbilleskiy, gosudarstvanty7 universitat im. Stalina. Pred-
stwileno eblenom-korrespondentom Akadsmii V.I.Mamasakhlionvym.
(Particles, 31"mentai7-Scatterir)g)

Z/. '16-0 0 67253
e4 (.,)
AUTH ON -31 __TavkheUdzg, A._ N ,Todorovt I T 9 SOV120-129-4-15168
Chernikovj No At
TITLE: The Spectral Properties of the Green Function in a Model of
the XU n Fi 1d With a Fixed Source
PERIODICAL: Dokl:ady Akademii nauk SSSR, 1959, Vol 1299 Nr 49 PP 769 - 772
(USSR)
ABSTRACT: First, attention is briefly directed towards various models of
the quantum field theory. If in Chew's model (Ref 3) the nucleon
spin is not taken into account, and if meson energy is assumed
not to depend on the momentum, the investigation of this model
is reduced to the solution of a system of two ordinary differ-
ential oquations of second order. In the present article the
properties of the Green function In such a simplified model are
investif;ated, It Is shown that, in the case of a rigorous treat-
ment of the problemp no paradox& of the type of "negative pro- /
babilitios" occur. The Hamiltonian of the boson field with a
fixed fermion source has the following form in the oharge-sym-
metric theory:
Card 1A

67253
The Spectral Properties of the Green Function In a BOY/20-129-4-15/68
Model of the Meson Field With a Fixed Source
- X(?" + + + + 0+ 0
P ~p t;Tn) + 7V)k(-~+i Ak + Bi Bk Ic k
9 Y- R f (A + + + + + I + +
' ~, + 7,- (Ck + Ck)(Tp fp
0 k k k + K + Vt.
f+ +)
*,I. Here Ak, Bl,, and A~t +1 and Ck denote the anni-
n Ck ( + 1~
hilation operators (production operators) 9f the positive,
negative, and neutral mesons; and ~ (~'r and t*) - the anni-
+P n p n
hilation operators (production operators) of the nucleons;
F2 ' R - the form factor of the nucleons. The proton propaga-
(jk k
tor mair be written down in the form 8(t-ti)
6
I , where M is an operator in
~ffp
dfH M
Heisen'berg representation: i dt .
. 'rho proton propagator may be written down in form of a %I
p +
scalar product. The operator of the nucleon number tp tp + ~+n +n
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672.53
The Spectral Properties of the Green Fanction in a BOV/20-129-4-15/68
Xodel of the Meson Field With a Fixed Source
has four linearly independent eigenfunotional two vacuum func-
tions, one one-nucleon function and one two-nuoleon function.
Green's function of the proton satisfies the equation
(E - Z)g(E) - ~oj where fo f' 10> is the amplitude of state
P
with a mathematical proton (t) is a solution of the modified
Sohroedinger equation i + ~06(t) with the condition
yt- 10
0, where t