SCIENTIFIC ABSTRACT GALITSKIY, V.M. - GALITSKIY, YU.V.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000614110017-0
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: July 19, 2001
• Sequence Number: 17
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

L
I
KOGAN, Vladimir Il ich; G LITI+S!l or Mi y oyic~j ZHABOTINSKIY, Ye.Ye.,
redaktor; TUMARA'". t' I ii Me stri roe WBr
1. ., e
[Collection of problems on quantum mechanical Sbornik zadach po
kvantovoi nekbanike. Moskva, Gos. izd-vo tekhniko-teoret. lit-r7.
.1956. 415 P. (KLRA 10:4)
(Quantum theory-Problems, exercises. etc.)

GALITSKIY, V. M. and MIGDAL, A. B.
"Dielectric Constant of a High Tempe
.Fature Magnetized Plasma and the Evaluation
of the Radiant Heat Conductivity." (Work - 1951); pp. 16i-iT.1.1
lf'.Phe Physics of Plasmas; Problems of Controlled Thermonuclear Reactions." Vol. I.
1958, Iniblished by INs.t. Atomic EnerL-y, Acad. Scl. USSR.
resp. ed. M. A. Leontovich, editorial work V. I. Kogan.
Available in Library.

AUTBORS: Galitskiy, V. M., Migdal, A. B. 56-1-22/56
,"ITLEa An Application of quantum Field Theory Methods to the Many-
-Body Problem (Primeneniye metodov kvantovoy teorii polya k
zadache mnogikh tel).
PERIODICALi Zhurnal Eksparimentallnoy i Teoretioheskoy Fiziki, 1958,
Vol. 34, Nr 1, Pp. 139-150 (USSR).
ABSTRACTs In the present paper show3, that the energy and the damping of
the quasi-particles depends on the poles of the dissipation
function of a ps~rticle. The author here investigates a homo-
geneous unbounded system, wherein the momentum operator com-
mutes with the Hamiltonian. In all Fermi-systems there ob-
viously exist excitations analoguous to those in an ideal
Fermi gas. It is convenient to study the properties of the
excitations by means of the methods of the quantum theory of
fields, by introducing the kernels of the system into the in-
vestigations. Apart from the kernels of the particles it is
also possible to introduce the functions of the dissipation
of the interaction between the particles, e.g. the kernel of
the phonon represents this dissipation function in the problem
Card l/ 3 of electrons in a metal being in interaction with the lattice.

An Application of Quantum Field Theory Methods to the Idany- 56-1-22/c/6
-Body Problem.
The kernel of the phonon determines the energy and the
damping of the excitations of the lattice. At first the
kernel C(pp) is written down for one partiolep and then -the
author passes over to a Fourier representation. Subsequently,
the properties of the kernel in the complex plane are,.in..
vestigated, and the-interrelation of the kernel of one particle
with the spectrum of the excitations is determined. The be-
haviour of the kernel at great positive times is also studied.
The energy and the damping of the excitations are determined
in the lower half plane by means of the real and imaginary
part of the poles of the analytical propagation of G(per).
The kernel for one particle also permits the determination
of other oharachteristics of the system, e.g. t',e distribut-
ion of the particles on the different momenta. Fir the pur-
pose of studying the energy spectrum and the beh-viour of the
system in weak external fields, it is necessary to inveBti-
gate the kernel for two particles. This kernel for two pLrt-
icles is written down here explicitly, it is suited, for ex-
ample, for studying the excited states of a system of N part-
icles containing one particle and one hole The case of
Card 2/3 forces of short range and the behaviour of a system in an

An Application of Quantum Field Theory Methods to the Many- 56-1-22/56
-Body Problem.
arbitrary weak electromagnetic field are investigated. There
are 3 figures and 6 references, 5 of which are Slavio.
ASSOCIATIONs IMbecov Ing1werbag wA FAWalcal lutiturte (Moskovskiy in-
zhenerno-fizicheskiy institut).
SUBMITTEDt July 12, 1957 (initially) and
October 24, 1957 (after revision).
AVAIL&BLEs Library of Congress
Card 3/3

AUTHORs Galitskiy, Y. M. 56-1-23156
TITLE: The Energy Spectrum of a Nonideal Fermi Gas (Energetichonkly
spektr neideallnogo Permi-gaza)o
PERIODICAM Zhurnal Eksperimentallnoy I Teoretioheskoy Fizikij 1958,
Vol. 34, Nr 1, pp. 151-162 (USSR).
ABSTRACTz The present paper determines the energy speotrum and the energy
of the ground state of a nonideal Fermi gas with a positive
potential of interaction betwoen the particles* At first the
one-particle Green function of the system is written down, A
formula is also given for the 3-matrix. In the d*velopuent of
the 3-matrix according to the powers of the Interaction 9 the
mean, values of the T-product of thelp-operstors occurs These
T-products can be represented in the form of a sum of the
normal products and the different groups of operators, Very
important for the further is the absence of a retardation in
the interaction. The second section gives an evaluation of the
gra-he and discusses the gas approximation,.Then the effective
potential of the interaction , the energy spectrum of the
system, and the energy of the ground state are calculated,
Card 112 where the course of the calculation is followed step by steps

The Energy Spectrum of a Nonideal Fermi Gas.
56-1-23/56
First an expression for the compact part of the self-energy
I is written down. Then the self-energy io calculated in
second approximation. The eriergy-speotrum of the system is
determined by the poles of the analytic continuation of the
Green function. Expressions for the energy and the atten-
uation of the quasip~rticles are written down. Especially the
excitations with high momenta, are investigated. The expression
found here for the imaginary part Im I makes possible the
determination of the chemical potential only in first &yproxi-
mation. The occupation numbers of the quasipartioles agree
with the occupation numbers of tho non-interacting particles.
Finally the graphs which were left out are estimated and the
higher approximation is shortly discussed. There are 6
figures, and 7 references, 5 of which are Slavic,
ASSOCIATION: Vb4cm 2091maring ad P1W510".MWU*sb (Moskovskiy inshonerno-
-fizicheskiy institut).
SUBMITTEDs July 12, 1957
AVAILLBLEs Library of Congreas
Card 2/2

AU12HOR: Galitskiy, V. M. 56--34-.4--40/60
TITLE: Sound Excitations i~,Fermi Systems (Zv-ukcvyye vozbuzhdeniya
v Fermi-sistemakh)
PERIODICAL: Zharrial eksperimentallnoy i teoreticheskoy fiziki. 1958,
7 1
Vol- 114~ Nr 4, PP- 10" - '1013 (USSR)
ABSTRACT: First the author gives a short report on references dealing
with the same subject. In Fermi. systems with attraction
sound excitations with small momenta are possible. These
excitatiQns are best investigated by the method of the Green
functiGn. The second excitations can be regarded as bound
sta+as of two elementary exoitations with a total momentum
different from zero. Therefc-re a method proposed by Gell--Mann
and F. Low (L,;,-.) -,an be ueed for oalculatl=3, Aroording to
this method the equation for the bound states is obtained by
elimination nf the inhomageneity in the equation for the
Gre(n function of the two excitations. In order to take into
account the structural change caused by t-he production of
the Bose c--.)ndensate of the bound pairs the original Ramiltonian
Cax*-,' with a dirqv-.~ interaotion among particles must be transformed

Scurid Excitations in Fermi System6 56~-34-4 .0116r,
by using a method de-Tsloped by- Bogolyubov (Ref 4). H=Eo + H Q+H',,
Ho E(p)(a+ a + a+ a = (,/2) r 2". 2 2'
0 Po P1 -~); E:(P) p
p ; Pi 0
is then 9'4talfied, where p denotes the Perni limit moment-amt
A- Ue"'/Q the quantity 9f the energy slit, and H1 the
Hamiltonian of the interac-titin among excitations. In this
case the zero.-th approximation of the Green functioa can be
regarded as sufficient. The interaction Hamiltonian R' in
f irst apprcximation contains only one graph f or the inter--
aotion betw~aen the excitations. The system of equations for
the Gr-:en funotions resulting from the elimination of the
inhomogGneity is wT.Itten down explicitly and the result ob-
tained can allso be applied to a system of charged particles.
The author thanks B. T. Geylikman, L. D. Landauv A. B. Mig-
dal and I. Ya. Pomernachuk for their valuable advice and
interesting dianussi~,na. There are 1 figure and 9 referenoes,
7 of wh'03h are Soviet.
ASSOCIATION: Moskowski~ inzhqnerno-fiz'Lcheskiv institut (VjQ0Qc_)v
ef 11hvuIcs and Engina-:iring-
I L ., . L
Cardl:2;4

-,-. '-'.
"Collective Excitations in Fermi Systems at Zero Temperatures."
report presented at the Intl. Conference on Many-Body Problems, Utrecht, 13-18 june ig6o.

,GA1ITSKTY V.M.
Fairing with other than zero moments. Zhur. ekBp. i teor. fiz.
39 no.4:1157-1159 0 160. (MM 13:12)
1. Moskovskiy inzhonerno-fizicheekly institut.
(Particles (Nuclear physics))

GOR'K91, L.P.; 2~ ~ITSKIY,- V.~.
Superfluidity in a Fermi system in the presence of pairs with
nonzero angular momentum. Zhur. eksp. i te9r. fiz. 40
no.4:1124-1127 Ap 161. (MUU 14-7)
1. Institut fizicheskikh problem AN SSSR-
(Superfluidity) (Fermi surfaces)

26717
S/056/61/041/005/032/030
13 1 L 2/B 1 -
NL, 0 1- 18
AMHORS.- Vaksy V. G., Galitskiy, V. M., Larl:in, A. I.
TITLE. Collective excitations in a superconductor
FE'aIODICAL: Zhurnal eksperimentallnoy i teoreticheskoy fiziki, v- 41,
no. 501), 1961, 1655 - 1668
TEXT: 1.Zuzqntum-fiold theory methods are applied to determine the spectrum
of' collective excitations in a sunerconductor. The collective excitations
are investi-ated by means of the Green functions for zero temperatures.
The excitations are treatEd as bound states of quasiparticle-s so that
their soectrum can be determine(! from the pole of the two-?article Green
function. The calculation of this function is based on the formal similar-
ity of th,. probleni to a one-dimensional relativistic one; The gap width
p1n,ys tht., role of' tho mass and the proximity of the particle eriergy to
that on the Fermi surface - that of the spatial momentum. For Ion,--wave
excitations the limiting frequencies and the dispersion of the oscill-q-
tions are determined for any momentum 1. First th,~ relativistic formalism
is developed for the theory of superconductivity using P. L. Gor1kov's
Card 1/8

S 26717 32/030
/056/61/041 '/005/0
Collective excitations in. -Bl02/BI38
three types of Green functions (ZhETF, 34, 735, 1958). The real phase
constant A is given byA = -i D(p-p I ) 6 d4p,; 1 _igo d2 D
P12 2 2
-1-1. +A ~ p +
nn n n I/pl; D is
90 =' Q ~ D (nn dn'An, D (p -p I D (4-*- -" = ;/p, -* - = p
Dhonon Green function. The Bethe-Salpeter equation for the two-particle
Green functions whose poles determine the excitation specta-Um is writtc-n
in weak coupling approximation.
(p+_~_ T3)1.,(T30(p_ k
T [(0 2.) 7)).V +
+ (C'0 (-~ P + '* Tb),,,. (146 (- PNN I
, 2) T)).,,] X
X 44p'[D(p-p')I(,,.(pl,k)--!D(k)TI.SpT-I((p,,k)j,
2. (25)
with
01 01 to
= 1 0), T$ (o 0 (6)
T3 1 0 T4 T, = (0 C=(OCU-00U
Card 2/8

Collective excitations in ...
267
S/0576671/041/OOD-/032/038
B1
B102 Bl")B
is found -.,,hich can be solved only for certain rel:itions the
energies k0 = w and the momentum k of the excitution dete-riAning the
r -, c t r um (A) (1, First the case k 0 is treated. Here the eenorul
8
pL
ormul as
Im
(L + P'f)tt,.,K,,. + 2A )A
-i- fjj,n,N3 . + -L (q3n,,,Frl Kim
-28.opD(k) "' fmoI(-M'#
.2&
M,
in zg" (f + !L~)tl""Kzm + q,(q"-q3hI MIgn, F
2& q3 -43
2
1(3
pD (k)
+28.0 f + 5:!9 )IOD
q
(q3I)ujrnKj5gnj - q4 0 3" 3
gt, JK K4
2A A .. I _ 92 +
qs qsf 'K3
+ 26.opD (k) q.,
NO
Gard 3/8

,9671
S ~61/041/005/032/038
Collectivu excitations ill ... B 102/B 138
With 7. =--knu, q,,= io), q2 q32 + qj', p2 q2/4W, f (P) are sin
(31)
change into -- -----
90 ff.' + f (g. - 2pD (6), 0)) X030 = 0.
TA-2 2A (321
90 1(-0 fi(050 - (I + gj - 21pD (o). 0)) K030 = 0.
2A
and for frequencies with 1 / 0 into
10
IM = 91 (L + -2!-f) K11. + g, f101.'
4A' 2A (33).
101. = g, fK51M - glfKsim
..2A
2(g _g )-l