Equations lot the Green Functions in Quantum Electrodynamies

Y P A B H E H H , q ~ , 7 I g . O Y H H I ~ H ~ I F P H H A B R B A H T O B O I T I 3 . J I . E H T P O ~ H H A M F I H E

(Co;~ep~aHile npe~bI2iymefi CTaTSII)

JA:N" FlSCHEI~ *) 06~eOur-te~bzgt u~cmumym stOep~b~x uec~eOoea~tufft, JIa6opamopu~ meopemuuec~oYt 96u~unu

,~y6na, CCCP

Hpe~aomel~ilbIfi BepecTeili~ii~ n Fa~aii~IIILIM ~LIBO~ ypam~en~fi ~na ~ym~II~I~ FpiiHa Hil3mero Ilopa;IKa [5] o6oSmaeTcg ~nK cnygag o6mero ~ncna gaeTiiII. Hart II3ISeCT~O, IS cay- ~ae o~Bofi ~IaeTil~ nonyeaeTca eilCTeMa ~isyx ypaisilettilfi (2), (2'), tr co;~epmnw wpn HeaasncnMHX ~yaK~n~ G ~ G I~ G tl, waK" ViTO ~JIa NX onpe~enenila npnmaoc~ 6H ~o6a Is:gTb ypaisHeH~g 9~n~ 6onee IsmcoIinx ~ y i l ~ r f ~ FpHHa II, Is ~o~ge ~oH~ois, pemaTb 6ecilo- HegHym peNyppeHT~y~o C~CTeMy ypaBHeiiilfi. 3TOrO MOm~O na6emaTs, ~a~ IloKaaa~ mBs~rep [1], ecnil ISISeCTg S aarpanm~a~ Isaa~Mo;IeficwmCs (L) ~yHmmn Is(x), ~(x) ~ ~(x), oil~c~sam- mge COOTISeTCTBeiiHO sHemnne saaceseecIr IlCWOqHiiI~II (~OWOltHOrO II ~ae~wpoilno-noaiiwpo~- Iloro noaefi. TasgM oSpa3o~ Isce ~ y ~ g s g rp i lna CTatIOISItTCIt 3aisIICIIMt,IMtI OT I#, ~2 II ~ B pe- 3yabwaTe ~ero one 6y~yw csasagb~ apyr c ;IpyroM COOTilomenn~Mil Tilna (jr). C noMombm 9TIIX COOWilOIlIeHnl~ MOmilo I13 (2') IICHJIIO~IIITb G 11 II Tall Ila6emawb pe~yppenTHOfi CilCWeMbI ypas~eiiilfi.

B 1954--1955 r r . 6~ao no~asailo, ~wo ~na SblisoJ~a (2), (2') s ~aa nepexo~a tr (3), (3') ;~ocTaTO~IIO Isocuo~baoisar O~HOfi WOab~O ~ y i l ~ s e f i Is(x), CosceM He ISISO~a V(X) S ~(X) (c~. [3, 4, 5]). OTO HMeeT aHa~e~ile nOwoMy, ~ITO qbyils:ninn r/ ~ ~ He IIMelOT flCIlOFO ~I311Hec- t(oro CMl~Cna.

B IlacToumefi CTaTt, e 3Ta npo6aeMa paccMaTp~isaeTc~ Is o6meM cny~ae 5on~moro ,mcaa :~aeI~TpOHOB II q~0WOHOm 06o6meiiileM CIICTeMH (2), (2') aisaaeTcs CIICTeMa (6),(6'), cojIepma- maa IlgTl:, pa3IIHX ~yn~m~fi FpnHa. qTO6t,I H36emaTb 6eciloHe,mofi pei~yppegT~Ofi CIICTeMIgI ypaisile~ilfi, neo6xo~ii~o tlCKJllOqlITb Tpn n3 HnX. 0I~aa~isaeTcn, qTO ecJIi~ OTI~a3aTbcn OT V II ~ II tte ISISO~tITI~ npil aTOM n a ~ x - H ~ 6 y ~ s )Ipyr~x ~y:u~a~fi, npoMe I~, TO pacqeT IseJIeT

JIoisoa~no C~OmHOMy ypaisHeHilm (7'). C Jlpyrofi cToponsL ecnn ISISeCTg IS narpa~m~as , ~poMe Is(x), BnemH~fi a~enTpOMar~TilbI~ noTeilgnaa ~I#(x) (CM. (L")), To I loay~TC~ 6oaee npocwoe ypaisile~ile (7"), noTopoe IsMecwe c (7) Ilpexcwallnslew co6ofi aHa~orileHym cgcweMe (3), (3') CIICTeMy ypaisHesilfi, coaepmamyD WO~nO ~ise paaailgH~x ~ys sg i l~ rpsHa.

Ho cpaisileiiilm c (7), (7') cilcTeMa (7), (7") o6naJIaew JlisyMn rJlamtbiMil npenMymecTisa~m Bo-nepisb~x, ~a Hee Isnonne Ilc~nsD~eH5~ ~aeH~ co;Iepmam~e s~ail~oJ~eficTisile, ~o~op~e IscerJIa n p n ~ n a m T npg p e m e g ~ ypais~eiiilfi ~an6onbmile Tpy~ocw~, g aaMeilenb~ nne~aMil c qtSyiiRgnoHan~M~ Ilpoilaisoa~iMn. HeCMOTpU na TO, nWO q)yHKgilo~aasn~ie ~ii~q~epen- gnaabn~e ypaBneiiiln MOmHO s HaCToamee IspeMa pemiiT~ TOnr~Eo B He~oTopBIX gacTnr~x cnyqagx, Bee me OTII1V[ ~cKnmqeH~eM ~aila Ilp~ii~nnilan~HO BOSMON~IIOCTI) 060~TnCB 6e3 Teopnn ISO3MymeHH~ n ~B[pa3iiTb pelneHne Is aaMIIHyTOY[ Isil~e.

BTopoe npeiiMyigecTisO aaIinio~laeTca Is TOM, ~I~o OT CIICTeMI~I (7), (7") MomHo aerI<o nepefiTil i~ O;IIlOMy qbyHngno~ansiloMy gzd)qbepeilgnan~iloMy ypaisHennm sblcmero nopamca, IlOTOpoe co~epm~IT TOJII~I~O O~ily ~yiiHI](illO P p ~ a (CM. (9)). Oilo 7IBnFIeTCg aOisOJIbilO eJIOH<BbIM, IIO ero MOmilo (ii IsMecTe c HnM Isce ocwaJn~Hl~le COOTilomengga) 3HaHldTenl~gO yiipOCT~TI~, ecnil IsocnonL30isaT~,Cg ~pyriiM Oillpe~eaenileM ~OTOnHOfi qaCT~l (~yill<I~I4ii Fpiiila (CM. (i0) n pilc. 1 II 2). Tor~a BMeCTO (6') 6yJ~eM IIMeTI~ O~HO II3 ypamteHilfi (11), (11') ~ (11 ~) (Is 3aislICIIMOCTII OW 8), ISMeCTO (I) II (~) - - COOTHOIIIeHIIH (I ' ) II (~ ') , ISMeCTO (8') - - O~HO II3 ypam~e~mfi (12), (12') n ISMeCTO (9) - - ypaisileH~e (13) Ilnn (13'). MomHo Ha~e~w~c~, ~TO ~o~xo~amee ~aMeile~ile onesmponsog HaCTII ~yIti(giln F p ~ a npiiiseXeT i( gan~gefimeMy ynpon~e~mo ypais~e~n~.

HocTyilnao 30. 12. 1957. Re]erences -- ~'7umepamypa

[1] S c h w i n g e r J . : Proc. Nat . Acad, Sci. USA, (1951) 37, 452. [2] CDpa~ii~ii E. C.: XAH u 98 (1954), 47. [3] A n d e r s o n J . L.: Phys. l~ev. 9~, 703 (1954). [4] I I o n i l s a H o i s M. H.: ~ A H CCCP 100 (1955), 1061. [5] B e p e c w e g ~ i l f i B. B., F a n a ~ i i i l A. ~ . : IXpo6~eM~ COispeMe~HOfi d)gsg~g 1955,

N o 3 , 1. [6] F r e e s e E.: Zs. f. Natur forschung , (1953) 8a, 776.

M a t t h e w s P. T., S a l a m A.: Proc. l~oy. Soc., (1954) A221, 128.

*) IIocTOI:IItHLII~ a~pec: Og3~sec~f~ IIItCTIITyT q C A H , I lpara .

Czechosl. Journ. Phys~ 8 (19S8) 389