CONCERNING THE INVAHIANT CONSTRUCTION OF THE QUANTUM THEORY OF A FIELD

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00039R000100110010-8
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 5
• Document Creation Date: December 22, 2016
• Document Release Date: June 8, 2012
• Sequence Number: 10
• Publication Date: March 5, 1951
• Content Type: REPORT

Declassified in Part -Sanitized Copy Approved for Release 2012/06/08 :CIA-RDP82-000398000100110010-8
Titl?~ CONC ~' NO T~~ ~ INV~iIANT CONS',~RUCTION OF`~ ~ Ul~'IU~ T~~ORY OF {l
FI~ by N. N. Uo~;olyubov~ V. L. Sonch-~vycvlch and n~ V.
asedvedev (USSR)
Source; Dokla Akaderr~i N~SSR Nov ~ a Seri a~ Vol LXXIV~ No 4~
~p -~b9~,~e~.~n thrioo-mont p~rio oal
CONFIDENTIAL
Declassified in Part -Sanitized Copy Approved for Release 2012J06/08 :CIA-RDP82-000398000100110010-8
 Declassified in Part -Sanitized Copy Approved for Release 2012/06/08 :CIA-RDP82-000398000100110010-8
50X1-HUM "
GQN~~ftNINQ TNT; ~NVARIANT CONTRU~TIC~N 0~~ T QUHN`rt~ '~NtaQ~~Y Q;' A ~'Tk,Lo
N, H, 9ogolyubav, Corr Memb load Soi U9dB
V, L, Bor~o~~#Bruyavioh
B, v, Medvadvv
The ropeeted attempt~-to aonstruot a quantum thoory of s Pield whoso rol-
~~~
etivistio inv~urie would not be purply illusory end in which it ~~ould not
be rieaesAery to report to physically aboard consequences with the holp of ~-
ao-called "doduotive formalism" havo :got last with suaoess, There~'oro, we hevo
undertaken in this work a dotailed investigation of th~o conditiono imposod on
ar~r quantur~- theory of a field bplely by the requirement of rvlativistio inver-
inr~ ~ ~ '"`~c write thcv~ conditf~oi~s i? ~ha Form o:' the well-known pArmutatiun
relationships:
H~ D a
R
A .~ ~ a ~ cf J
~' N ~~ ~ ~ ~~ ~fh~M~Yh
~Cere H, ~ ~ M and I~- are b~e~~operators, re~peotively, of energy, =~'
fie, moment, and the time part of the t~-moment (n ^ a ^ 1).
It is easily seen that all the relationships (1) are not independent
For example, all rer~ainir~g relationships ar? consequenoes of the relationships
a 1~ ~ Therefore we will consider only the relationships of the fis~st
(l) '~ ~ ~ r
group,
The relationships (1) were recently studied by Dirao (P, A, M. Dirac,
~tev, Mod, Phys, , 21, 392, 19~r9) For the ca?e of the classioal theory. We
gill consider them within the limits of th? method of secondary quantization,
'Ne introduc? the ordinary operatores a~,, a~ , conforming to the permutation
rulers
(2)
(for simplicity, we restrict ourselves to the case of 4~ dose statistics ).
Thos index ? is a combingtion og signs m and M, the first of which is the or-
dinary wave v?otor, while the second oharaoterizes the nature of the field,
~~ ~ ~ ~ ~
~.
~.
Declassified in Part -Sanitized Copy Approved for Release 2012J06/08 :CIA-RDP82-000398000100110010-8
 Declassified in Part -Sanitized Copy Approved for Release 2012/06/08 :CIA-RDP82-000398000100110010-8
~uNfIDENTIAI
the aharga, t~~o r~ombor oP tho pompon?nt, oto~ In tho~o oaaoo in which ~ tekte
X14 ~i~'ywv'-1
on diearoto v~-luoa, tho dymbol d~(~ ~: ~~ ~Yo daaignoto
lT~ ~ ~
,/ ~, ,
~'re wili aloa~uao the a bola ( ) ands to deoignate ay~amotry and
Ym
~.torna#~ion, reopeotivaly, with reopeot to tho indices in the parentheaR~ ^x
braokete
we will consider that any operator oncountered ire the theory aan be ex-
preoeed through a~, anal a and oonoayuently can be writton in tha ~a~s
~ ~
~ti ~~,
w
~~~ ~~ ~ ,, , , , ,~1 r are a ~i~atric with ree act
where the Functions P~(~1,, .. , , ~_ ~~t ~,), A
.. f M{ ~~
to perruutatione o~ the argur~te within each group i/ W oe~ show that the
commutator of two operators ~ and G of the typo (5~ nas the Forms
A
whore
0o r- t
r ~ ~ ~~ ~
v, r .~
~ ~ ,~o
h ~ w+ ~ U
!~/
~ r~ , ,
Jhr ~t ~ -
1 ~
,, f ~ L~,~,,~
x
~, l`rs. ,,~ X71
X
In con.For~.ir~ with the above, we write ~~e operator? pa ~ ~C' I~ in the x'07 ~;
From the r?lationships (la) and (ld), we 0a8ily ob'~ain;
where (?)p E M)m~,~ an~ E(M) E ? 1 according to ~;;~ sign of the charge
H
.~.
~{~" .1
(~b)
Mil r/
...~
... ~,
1 Z ~ k ~,
Declassified in Part -Sanitized Copy Approved for Release 2012J06/08 :CIA-RDP82-000398000100110010-8
lr- t t/ ~ ~e ~ .>~
(whero the prime indicates differentiation x~th r~ ~pec;t to the entire argument)
A l ~-k ~' ! ~ a~T
~ ~
 Declassified in Part -Sanitized Copy Approved for Release 2012/06/08 :CIA-RDP82-000398000100110010-8
GOf~FIDENTIAI
~o~~ (la) it follows theta beaa~uoa of (7), (~), (9), and (10)t
~?~ r?~
~,,..,
where
~ ~ ~r~~~~~~~ ~r~~~
n~~
~, , ~, ,~
~ ~' s '" ;: ~ ~ t ~h ~ ~ ' h`~,
~ Yl l
r
~
/
~
~
~
V
,
o t
si
~ i
~
~
r