SCIENTIFIC ABSTRACT SUDAKOV, V.V. - SUDAKOVA, V.

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• Document Creation Date: November 3, 2016
• Document Release Date: August 26, 2000
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• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

SUBJECT USSR / PHYSICS CARD 1 / 4 PA - 1921
AUTHOR �jDA1@QVjy.V_
TITLE The Conclusions to be drawn from the Renormaliability of Quantum
4lectrodynamics and the Meson Theory.
PERIODICAL Zurn.eksp.i teor.fia,31,fasc-4, 729-731 (1956)
Issued: I / 1957
According to the author's opinion these conclusions drawn from renormalizabil-
ity (M.GELL-IWIN, F.F.LOW, Phys.Rev.21, 1300 (1954), N-P.BOGOLJUBOV, D.VAIRKOV,
30, 77 )(1956) are best formulated as follows:
a (g 2 () ) P (g2Pj) a (g2
(X(g 2, - C C P(g2 j-L C a d(g2 -L) C C
0 a (E 2 0 (g2L) 0 d (g2 L)
C c C C C C
Here aC, PC , dC denote the asymptotic expressions of the slowly modifying fac-
tors in the case of a renormalized summit part and renormalized GREEN'S func-
tions of the nucleon, g C - the renormalized meson charge, ,
I = ln(-k 2/m2) , L - In ( A2/M2) ( A is the "cut off momentum", ct,p,d and g 0
denote the not renormalizable quantities which correspond to the cut-off
momentumA -
It was found useful from the beginning to introduce the logarithmic variables
and L. Apart from the trivial conclusion that a, 0 and d become equal to
le at t = L, the following postulate results which is of importance for what

I Pk - 19:?1
Zurn.eksp.i teor.fis,31,fasc-4,729-731 (1956) CARD 2 / 4
is to follow: withj>/1, CXY P and dare asymptotically the functions of the
difference f - L - ln(-k 2/4 2) alone, i.e. they no longer depend on the
nucleon mass m. Further, a quantity is introduced which may be called "effec-
tive charge":
2(j ) 2a2(g2, 2 2
9 _g @-L) P2(g2, @-L)d (g2,j -L)- g2al(g2,@ ) P (g )d (g2,@
0 0 0 0 0 C C 0 c
This equation results from the aforementioned relations and rom the relations
between the renormalized and the not renormalized charges. From the last named
equation it may be seen that theeffective charge g can be looked upon either
as a function of g 2 and or as a function of g 2 and The final formula-
0 e
tion consists in the statement that the logarithmic derivaiLves of a and a 4@ etc.
according to t depend only on the effective charge:
2 g2) 2
al/a = a,/ac = Fl(g ); P,/P P,/Oc = F dI/d = dc (g )i
c c 2( 3
(g2 Ig 2 . 2FJ(g2) + 2 F 2(92 + F3(g2)
The strokes here denote differentiation according to the corresponding argument
- L or . The last equation is a consequence of the first three and also
of the second-named equation. As an example the first of the three equations is
provedi the others are obtained in the same manner.

V
Zurn.eksp.i teor.fis,.L1_,fasc-4, 729-731 (1956) CARD 4 / 4PA - 1921
a - Q1/5 , P = Q_ 3/10; d = Q-4/5 are obtained.
In the most simple case of quantum electrodynamics and if the series of the
perturbation theory for GREEN'S function of the photon:
d = E@ c e2m (f -L )n is known an asymptotic expression for dt can be
t M;@, mn 0
obtained in any order with respect to eWith the help of WARD'S theorem the
following is obtained for quantum electrodynamics:
2 2 2 2 2, '/dt ',,,-.P(e2)'/e22)
e e dtt (e ,t - L) - e dt', (e ) dt -dt - F(e
0 0 c c
By investigation which is similar to tJ above we obtain:
2 2m 00 2m
F(e ) =f cmi , / 2::- Cmo e
m--1 M=o
When determining the aforementioned series for dtthe cut-off proceeding de-
monstrated by D.7f.POSENER and M.W.P.STRANSBERG, Phys.Rev-22, 374 (1954), which
warrants the condition dt(e20) = 1 being satisfied with accuracy, must be
used. 0
INSTITUTION:

Y
Zurn.eksp.i teor.fis,,31,fase-5,899-901 (1956) CARD 2 / 4 PA - 1931
P denotes a quantity which is connected with the amplitude P of scattering
by the following, relation: (g2 /411 @ ) P, @ C. (g 2/411@ )PC. A is a
0 0 a c 0
Constant in the following term of tho UMILTONIAN of Intoraotion;
0/41 ) (6,1112 6 IT3T4+ 6 T1 'r3 12 T4 + 6r1 Ir46T 2T 3 1 T'r2 T-T3Tr 4*
The equivalence of the definition of the effective charges by renormalized
and not renormalized quantities follows from the aforementioned equations
and from the following relations between renormalized and not renormalized
constants: 2 . 2 a2 (g2' A ) P2 (g2'A 2
go ge a C c, L C C c L) d C(gcl@ C. , L)
0 . -A d 2 (g2' , L) P C (g 2 1 @ Q
A
C a G Ac a c
The fundamental statement made is that the logarithmic derivatives of 2
a, P, d, P according to are only functions of the effective charge g
The proof of the aforemeltioned equations is slAched out'in short. The
logarilbsic derivatives of the effective charges are:
(g2)I/g2 =2F 1(g 2, @) + 2 F2(g2, A) 2 F 2(9 2 3 )+ F 3 (g2
= F4 (g2'A j + 2 F 3(g2'A J. If F is known these two equations form a
system of differential equations which, together with the boundary conditions

Yurn.eksp.i teor.fis,.L1,fasc-5, 899-901 (1956) CARD 4 / 4 PA - 1931
The following equation for the amplitude P of the scattering of a meson by a
meson is eventuall obtained:
1 2
,dP/dx - 16/3 - (11/'6)(P/x). In addition there is the boundary condition
PM - 4n A 1g2 . The solution of this equation is:
0 0
16 B - x-19/3 1
P x ; B - (1 +
B + (8/")X-197-3 92 1T 92
0 0
which is in agreement with the results obtained by I.T.DJATLOV and X.A.
TER-MARTIROSJAN, Zurn.eksp.i teor.fis,30, 416 (1956 for A 0 . 0 (B - 1).
The here discussed method5of investigation are suited for the determination
of asymptotic behaviors of any order with respect to g2, A , if the results
of the perturbation theory are available up to and including the corres-
ponding order.
INSTITUTIOTT:

Dokl.Akad.Nauk 111,fasc.2, 338-340 (1956) CARD 2 / 2 PA - 1960
Next, the computation of the contribution made by each single part is dis-
cussed in short, after which the amplitugg of the scattering of a meson by a
meson is expressed as follows: 11(j) - 7- 2-N 2: f (f).
N-1 n nN n n,,.".,n,
0 of he type ni. The to-
Here fn denotes the contribution of the i-th par i le
tal amplitude P is expressed by a sum of 6 squares (which are illustrated) and
by the sum of the three F(J), which correspond to the totality of diagrams re-
ducible in a certain manne : P - RO(j) + 3F(@)- The following expression
is in the and obtai@ed, L 2 2 g2 -1/5
P Ro(@) - (39018;) P (z)d (z)dz, R,, M 240 - x),x=[I+(5 o/41t)(L-1)]
The derivation mentioned Fiere can be generalized with only minor complications
(connected with the occurrence of isotopic indices) for the symmetric pseudo-
scalar theory. The expression for P(j), which corresponds to this case is
also explicitly given. In this case he integral equations are reduced to
differential equations and their exact solution, i.e. the expressions"or P(x)
are also explicitly written down. These deliberations point in the direction
of the meson charge being equal to zero.
INSTITUTION:

I - ". i
1;@Il ;.L, I
. ---
L
- 1. -, :-@ Z- ,

\ 11,,
cv')
C;6
5
AuiHm DUTWVp I.T., -kPAMV, V.V.,, TBR-UaTU10S!Z'j K.A.
TITLE The Asymptotic The6@5 @e Scatterir-, of a Meson By a Meson
(Asimptotichaskaya teoriya rasseyaniya mazona na mezone. Russian).
PLRIODIGAL Zhurnal Eksperim. I Teoret. Fiziki, 1957, Vol 329 Nr 4, Pp 767 - 780
(U.S.S.R.)
ABSTRACT The paper under rikiew determines the asymptotic beha*r for the anp-
litude of the scattering Of A MS@nn by a Meson in a theory of the type
of the theory devi"d by Landau,, Abrikoaov and Khalatnikov. First of
all, the authors of the paper undergreview demonstrate that the sum of
the contributi*m of all ieducible graphs satisfies an exact integral
equation, the form of which depends only on the contribution of the
primitive gr&phs, The computation is carried out step by step, and the
integral equation obtained is written down In tie explicit form. With
two additional analogous ecpations a system of three integral equations
is obtained, this system defines the functions F(k,, k 25 9 k ); F(klp
19 44
k
k
tit
k
k
k
k
k
bi
l
b
th
d F(k
)
)
an
unam
e
n
an
guous
y
y
y
2,
3,
2,
,.,
4,
4
3
R (klj k 20 @ k e by the contribution of the primitive graphso
'
@'
fl@
i
;
I

a
n is specialised for the case of high impulses
n the in
T
o
t
qu
for the neutral and for the symmetrioal theory* In the symmetrical theo-
ry, it is possible to elsiminte from 'cons idqation the variables ofthe
isotopic spin of the mesona* The total sum-,,'P@c) of the reducible gophs
Card 1/2 is a finite quantity of the am@ order of m@jnltude as the contribution

56-'@-18/52
ASSOCUTION
PRESENTED BY
SUBMITTED
AVAILABLE
The Asymptotic Tbeory of the Scattering of a.Meson By a Meson
R of the primitiye grAphs, Finally the paper under reviev d1acusses
tHe properties'*f the'renormalization of the Amplitude P of the scat-
tering of a meson by a mes'one #.t L+ -, it is possible to automatically
normalize the expressions for the sums P(x) and P(@ ), without being
forced to introduce into the Hamiltonian terms proportional to 5F 40
(7 reproductions),
Not given
17 December 1955
Library of Congress
Card 2/2

KOLKLTIIOV, V.A.; 0=1, L.B.; RUDIZ, A.P.@ SUDAKOV, V.V.
Position of the nearest singularitieu of the 7@fl- scattering
amplitade. Zhur. eksp. i teor. fiz. 39 no.2:340-344 Ag v60.
(HIRA 13:9)
(Field theory) (Scattering (Physics))

SUDAKOV, V. If.
Cand Tech Sci - (diss) "Application of gamma-radiation in testing
building materials and designs." Leningrad, 1961. 17 pp; (Lenin-
grad Order of Lenin Inst of Railroad Transport Engineers imeni
Academician 1'. N. Obraztsov); 150 copies; price not given; (KL,
5-61 sup , 193)

SUDAKOV, Vasiliy Vasillyevich. inzh.; KOMOVSKrY, M.F.9 inzh.9 red.; FREGF.R,
-61MAP I.A.p tekhn. red.
D.P., red. izd-va; BEibG
[Using radioactive radiation to control the density of building
materials] Primenenie radioaktivrqkh izlucbeni:L dlia kontrolia
lotnosti stroitellrqkh materialov. Leningrad. 1961. ;f P.
eningradskii Dom naucbno-tekhnicheskoi propagandy. Obuibn peredovym
R
opytom. Seriia: Stroitellnaia pro4shlennostZ-9 no.5) (MIRA 14-.7)
(Building materials) (Gamma rays-Industrial applications)

AUTHORSs
TITLE3
89-222
S/05 61/040/001/028/037
B102YB212
Patashinskiy, A. Z., Rudik, A. P., Sudakov,---T.-V-;
SingulAritibea of scattering amplitudes in the perturbation
theory
PERIODICALt Zhurnal eksperimentallnoy i teoreticheakoy fiziki, v. 40,
no. 1, 1961, 298-311
TEXTs A study has been made of the position of singularities of the
scattering amplitude and its asymptotic behavior in the perturbation,
theory. Due to conservation of the four-momentum of scattered particles,
the four-momenta of the scattering and virtual particles are located in a'
three-dimensional space for any perturbation-theoretical graph. The three
linearly independent four-vectors are chosen for basis veotorst W p1+P20:
2 2
pl+P31 P - p,,ip,,. For p Mi (i-l,..4)
2QIW - MI - MI M + MI, 2WP = Mil M'2 + M2
I I M32 - I
2 + M2 MI - M" + M. (1.2) holds.
Q2 + WS + P2 M2 + M'2 + Af2 2.
2QP =.MI 2
Card 1/5

Singulgrities of sciattering...
3/056/61/040/001/028/037
B102/B212
The scattering amplitude is characterized by six parameterel for con-
M2 2 2.-
venience they are chosen to bet and the invariants W and 0. Only the
singularities with real invariants are considered. There is a certain i
2 2
relation between W , Q. and the masses of the virtual particles at the
singularityl this relatien is ch raoterized for graphs of the type shown
in Fig.1 by the ratios between P and the squares of masses of virtual
V3 i