SCIENTIFIC ABSTRACT SHIROKOV, YU.M. - SHIROKOVA, YE.I.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001549530003-1
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: August 23, 2000
• Sequence Number: 3
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

3/05 62/042/001,1023/048
Invariant p,irametrization of the... B104%102
fina", states of the particles. This is necessary when examining rea'ztionr
s:th zero-mass particles, The conditions under which the scatter.Ing ma~r_~x
- Lnvariant with respect to space and time refleo:ticns are formulated
U.-:irig a unitary Lorentz transformation U the scattering matrix is
parametrized in an arbitrary (laboratory~ system: S lab ' U+S cms U, The
invariant parametrization of the relativistic amplitude for scatter:ne
through gi-ten angles is performed for reactions with particles of
arb'_trary spins The analysis is applicable to zero as well as nonzero
r~6t mass particles. There are 15 references: 11 Soviet and 4 non-Soviet
T~,e four references to English-language publications read as fol',Ows:
A Simon. Phys- Rev., .22, 1050, 1953; M, Yacob, G. C. Wick, Ann. of Ph..s.
7, 404; 1950; L Wolfenstein, J. Ashkin.. Phys, Rev., Pj
Edmon"'d's. CERN, 55-20, Geneva, 1955. 947, 1952;
A"';SOCIATION: Institut yadernoy fiziki Moskovskogo gosudarstv4~~nnogo
universiteta (Institute of Nuclear Physics of the Mosrcw
State University)
ST-7 BIM I T T E DJune 6; ;961
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ACCESSION NR: AP3009492 S/0188/63/000/005/0058/0066
AUTHORS Lomskly, G S.; Shlrokov, Yu. M.
TITLE: New types of connection of local operators with dispersion matrices
SOURCE: Moscow. Universitat. Vestnl-~. SeriYa 3. Flzika, astronomiya, no. 5,
19063, 58-66
TOPIC TAGS: matrix algebra, mathematical operator, matrix function, operator
equation, vector function, vector calculus, matrix element, matrix, local operator,
dynamic moment
ABSTRACT: A method for obtaining S-matrices for'the' non-relativistic case by means
of a two-body Heisenberg matrix element of the local operator Is analy2ed at length
in the present paper. It is shown that the direct application of methods given in
an earlier paper by one of the authors (Yu. M. Shirokov, ZhETF, 44, 203, 1963)
allows one to obtain all the phases of dispersion except one, namely the S-phase.
In the present paper, a significant amplification of this method Is derived, allow-
ing one to calculate even the S-phase with a high degree of accuracy. until re-
cently, the only expression for the relationship between 'the matrix elements of
local operators and the dispersion matrix was the reduction formula of Lehmann,
Zimmermann, and Symanzik (Nuovo Gimento, 1. 205, 1955; 6. 319, 1957). Consequent-

ACCESSION NR: AP3009492
ly, it was assumed that matrix elements of local operators have immediate physical
meaning only in a mass envelope. The present paper is an amplification and analy-
sis of results obtained with particular application to the non-relativistic case.
Tne method of dynamic moments was used to obtain a dispersion matrix with the lo-
cal operator A(7,0 for non-relativistic particles dispersed in the outside fiel 'd.
Thus, the result of this analysis is the proof that the whole dispersion matrix can
be reestablished according to a given Heisenperg matrix element of any scalar,
local operator A(x,t) for the diffusion of one particle in the outside field. This
can be accomplished with accuracy up to the constant (i.e., Independent of the
energy and transmitted impulse) phase factor. The proposed method is suitable for
relativistic and non-relativistic cases. orig. art. has: 45 formulas.
ASSOCIATION: NIIYaF
SUBMITTED: OIApr63 DATE ACQ: O8Nov63 ENCL: 00
SUB CODE: MA NO REF SOV: 002 OTHER: :004
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e0 kr
9/05616~/044/001/03T
BI 12/M~~'
AUTHOR: Shirokov, Yu. go
TITLE: Microcovariance and-microcausality.ih the, quant~*';~:
theory
_k
PERIODICAL: Zhurnal eksperimenta.10noy-1 toorettohe*ikel.,~fii0ii-.-"..,--,-,~,,'.,, 14;A~
v* 44# no* It 1963* ~203-224
TEXT, Basing on the principles of the quantum' thobr~~, i6 --f02.
conditions are derived for microcovaTiancei and mioroolutslit~:`
universe is poeudc-Euclidean everywheral,an o0erAtor,T
V
obeys the law of conservation BT (x)/ax 0 and which- is-. dote rmillot..W~- N
11V
the distribution of matter in the Universee.-Within the' ilihi,.oonot ~t
condition 6T (x)/6g (y) 0 is fulfilled. With
AV
conditionap the quantities describing the spice - time- rielat 16i is-it
relativistic quantum theory are connected with quantities
momenta, which are directly suscaptible to experimentaVaeasuirsaiginte"'
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77.

'T'
6A
Microcova.riance %n4 microcau'salit 1-2 18C,"..",
ASSOCIATION: Inotitut yadernoy.*fiziki
universiteta (Institute of--Xuoleir-.~6 lai',-cf- Wi.
moscow'stato uniVersity)-l
SUBMITTED: July iol 1962
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4Z

L 0631-63 -EWT(d)/FCC(w)/BDS AFFTC- IJP(C)
ACCESSION NR: AP3003129
-9/0056/63/0"/W6/102/199
f AUMfOR: Cheshkov, A. A.j Shirokov, YUQ
TITLE: Invariant parametrization of local operetors~o
SOURCE: Zhurns.1 ekaper. J teor. fizild, v. ", no, 6. 1963, 1982o-1992
TOPIC TAGS: local operator paremetriz&tion, space-time structure, elementary.
particle structure
ABSTRACT: A general method is developed, with the aid of which the matrix elements.
of local operators of arbitrary tensor or spinor dimensionality, specified betweeni
states with either one or several particles of arbitrary mass or spin, are
expressed in terms of invariant form factors. The same technique as used by the
authors previously for parametrization of the scattering matrix (ZhETF v. 42, 144,
1962) is employed here, but is modified to allow also for the space-like 4-m=enta,
and to acccmmodate the possible tensor or spinor indices of the local operators.
The matrix elements of a scalar local quantity between the states of one particle
with arbitrary spin is first parametrized. The results are then generalized to
include the case of a local quantity having a nontrivial tensor dimensionality.
The procedure is finally extended to matrix elements of local operators for
Darticle systems.
Card A_asociation-_'_Inat,_0f Ilikelejr sics, Moscou St. Un.

:-.~:CESS_70N NR: AP4019224 S/0056/64/046/002/0583/0592
AUTHOR: Shirokov, Yu. M.
TITLE; Now reduction formulas
SOURCE: Zhurnal eksper. i teor. fiz., v. 46, no. 2, 1964, 583-592
TOPIC TAGS: quantum field theory, reduction formulas, 0 matrix
theory, matrix element parametrization, local operator, observable
quantity, local field, mass shell, Heisenberg matrix, scattering
phase shift, inelastic interaction, inelastic interaction channel,
one particle form factors, matrix element analyticity
ABSTRACT: This article continues developing a technique first in-
troduced in-another paper of the author (ZhETF v. 44, 203, 1963)1
which aims at a complete parametrization of matrix elements of local
operators by experimentally observable quantities, i.e., by elements
of the S matrix. It is shown that the method of the author, named
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AC CESSION NR: AP4019224
the method of dynamic moments, is capable of relating to the S ma-
trix not only matrix elements of local fields and currents on the
mass shell but also off the mass shell. The main result consists
in demonstrating that a given Heisenberg matrix element of a local
operator determines all the elastic scattering phase shifts except
one, as well as kinematic characteristics and transition amplitudes
for all inelastic channels. In addition one-particle form factors
of -the operator in question can be determined for all particles pro-
duced in the inelastic channels. The connection between this work
and the reduction formulas of Lehmann, Symanzik-and Zimmermann-is
brought out and some comments are made on the implications for the
analytic structure of matrix elements of local operators.
ASSOCIATION: Institut yadernoy fiziki Moskovskogo gosudarstvennogo
universiteta (Nuclear Physics Institute, Moscow State University)
SUBIVIITTED: 23jun63 DATE'ACQ: 27Mar64 ENCL: 00 -
SUB CODE: PH XO REF SOV: 004 OTHER: 003
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M4:-,eyev, V. S.; Shir-okov, 14. M. j
TITLEE- On
R"IE Zhurnal eksperirnental'nay i teomticheskoy fiziki, V. 48. no. 2, 1965,
7j~-722
T F: C an rt
7 A.-,-' i~~.iant-dm fi,-Id, scalar neutral qu tum field, spin pa icle
previously lescribed by Yu. M. Shi--okov for obtaining the
tesCr4ption is extended to tie
r- jeriv'-~' from the
qua-~":ti~s a
--i,A;'zi j', -f a -A.ar quar~'um field A(X) wh,,r-n are
-r~ ar. arbitrar-I basis a. Transitioa to a cor-puscuiar descrij)tion Tean.~
-ha~ one, deter-mines: aj the spectra of aasaes x and spins j for all stable par'ti-
:;et of quantitles 1(3 1 xjjklin, > Q
accordino to a power law. The spatial pressure distribution is described
by the empirical formulas
P - (9-75/00)"" at 0-0005,