THE ANTICOMMUTATIVE MATRICES IN THE MESON THEORY

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00039R000100140008-8
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 3
• Document Creation Date: December 22, 2016
• Document Release Date: April 16, 2012
• Sequence Number: 8
• Publication Date: September 12, 1951
• Content Type: REPORT

Declassified in Part - Sanitized Copy Approved for Release 2012/04/17 : CIA-RDP82-00039R000100140008-8
Titlat T1i ANTI00'IMUTATIVE NATRIOAB IN T
A11 3orgardt, Dnepropetrovok State Univev~ity#
Sources ao1c1ad f Aka~omii Nauk SSSR, Vol LO VIII , To 6 (21 June 2.9$1), p go 1113-4.
CONHOENUAL
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oxi -HUM
 Declassified in Part - Sanitized Copy Approved for Release 2012/04/17 : CIA-RDP82-00039R000100140008-8
U HF ID :itie;al
uT}Uj A ITICQ~ MUTATIYJ MATRIO~6 It TLi ME8O1 TIOHY1f
A Por~ardt,
I opropotroYek State Univiraitr.
50X1 -HUM
LNotos The 'ol1ow short artio1o o~me from the M themfttct1 Phyeioe oaotion off'
noklwly 1M{Momii Nau1 SSSH, Vol LUYZIZ, Ito 6 (21 June 191), P ea 111 ~ the ar-
bolo hnd been submitted 25 April 1951 by o,oad?miaian V. A. Pok.
The frst.?order wave oquationa for tho meson field can be written in the foxatl:
~M S B4i f 8x f ko+'a 0 (ko~ Eo f 'a ) (1)
where poi 4) is a uni-oolunui a&trix oontainiag tho components of the tensor cuun-
tities that oheracterise the fia1d. Tho matriaos Pi cntiefy the rupee of commutatio1 t
Ei 8k E1 El 3kk Pi Bi kl ? Pl S . o . ( 2)
In tho four.4imensiona1 apace there are three lrreduoib1o non-Ltolideen roi
prosontntione of this algebra: 1qt-row, 5..row, and 1.rowt the first rcproeontation
is undd to doncribe ~rootoriel (V) or pseudoveotorial (PV) field,, the second is for
the description of nonlar (S) or peeudosoalar (PS) field, and the laat reprenent~
tion Pi (0) is trivial
Employment of the reduaible 16-row representation of the beta algebra (10-row
plue 5-row plus 1-row) givee the wave oration for tt mixture of moaon fields (V . PS
or P7 S ndxture). It is possible to exp n this scheme by includir in tho general
wave equation a description of all four types of meson ?ieldn.
Let ua une the dinarr form of the raduoible representation2 and let un desig-
nate the matrices 3I eo that the wave aqcation oarree nda to the V + P5 mixture,
(1)
Pn ?aJ//87j1 + ): (3)
where psi ' ie a 16-component wave finotion composed of a scalar artcl oomponontn
of the four..dimensional vector and completely tntiaymmetric teneorg of firat, third,
and fourth rank; p1i ie the function characterizing the oo.urce of the field..
Prom thin 8qua.tion one aan obtain the wane equation for tLte PV s S mixturo by
way of a transformation of the functions 'and -P by nieatta of a 16-row Hermitian
matrix ra, which is oonneoted with traneforyntiona of the mirx*or.rafleation type.
The nou~ht~for equation will be C1)
- Pn a''/3xn + ko t '' C a)
where ~I' = ire, ' = it
( i t : ~~1r0, M i gti' ), s , $ . , , / , ! , . 1 . - C5 )
0
Prom these relations tli.t are given above it follows that CL.) is equivalent to:
4 koW* ..,,(4b), where (11)N ? C~~
, (6)
Thus the oquation of the form fin' /~xn + k' x ' (7),where l L 11)(8),
descx'ibea a mixture of the general type containing all the tensor f el e. The 16 ow
flerriitian matrices 1"i satitefy the sample commutative algebra. Actually, the matriu ?. u
CUNFIDkN 9 iN'~.
Declassified in Part - Sanitized Copy Approved for Release 2012/04/17 : CIA-RDP82-00039R000100140008-8
 Declassified in Part - Sanitized Copy Approved for Release 2012/04/17 : CIA-RDP82-00039R000100140008-8
CONFIDEi1
of traneformatione () and (6) of I'p Oeeeeeee the foiiowin 'o ertj
~ '~ ~ Oe~
r29 i, 3iro3k 4 3kZ'oBi 0, r
o o i' ~i3krI. cS'Io.
ik
Uain~ there rv1atione one can aaoi1y show that r ore onti
i oommn~ati9ot
*(rr'1) . Lk' Z $ o
Sinoe, moreover, one oo net (I 'j) ) o, it turnr o u
t that
(9)
ra : r1r2rr4 (11)
In the group of I'Lmatrices there are 16 m~trioal o eratore which
with c' and give the tensor denaitiee of the f'adnent in cttinatioo
the Mold, The ?norgy density, in the general a e sl P~'ei0al ~uax-titiea of
althov~h the Mold. even poaaeaoea late ral a ?~ i? not positively dofinit?,
thoory ie farmally onalo oua to tho ~ pia` The further depalopmoat of bha
theory of the electron. Voe of thin parafe1iam
can facilitate the solution of a number of probloma is tho theo of me
It in poaaib1o also by woy of ena1o~y to clarify the eioal cont eon fields.
unolear relations in the electron theo . ,Y ent of certain
A11I~SR~+10~6~
1.
N. $emmor, Proo Royal Sooiety, A, 173
92
1
(939)
3
2.
.
,
.
' ?
W. Pauli
Relativisti
Th
,
c
eory of Momentary Particles, Part II,
(book trenalatod into Russian at Moscow).
!i, 1947
CUtbll:IDUI1 ML
Declassified in Part - Sanitized Copy Approved for Release 2012/04/17 : CIA-RDP82-00039R000100140008-8