Gauge Invariance and Massless Gauge Particles in Spinor Theory.pdf

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1、ILNUOVOCIMENTOVOL.4A,N.221Luglio1971GaugeInvarianceandMasslessGaugeParticlesinSpinorTheory.H.SALLE~Max-Planck-Institut]i&PhysikundAstrophysi]~-Miinchen(ricevutol'lFebbrMoI971)Summary.--Itisshownthatgaugeinvarianccinspinortheory--achievedbyappropriatedefinitionoftheproductofthre

2、eyfsatonespace-timepoint--involvesvectorbosonsofmasszerowiththerespectivequantumnumbers.Thesebosonsareconstructedexplicitlyinfirstapproximation.Introduction.Itisawell-knownfactthatgaugetransformationswithspace-time-depen-dentfunctionscanbeincorpora*edinatheory--e.g,eleetrodynam

3、ieswithDiraespinors--ifweintroduceatthesametimeavectorfieldwiththequantumnumbersgivenbythegaugetransformation.RecentlyDtiRRandWI~TEI¢(1)haveshownthattheinteractioninaspinorequationcanbedefinedinsuchawaythatwegetgaugeinvariancewithoutexplicitlyintroducinggaugepar-ticlesofmasszer

4、o.Itisinterestingtoseethatthispossibilityisconnectedcloselywiththearbitrarinessinthedefinitionoftheproductofseveralfieldoperatorsatonespace-timepoint.Thequestionisraisednowiftheinverseistrue:Doesthereinsuchatheoryexistnecessarilyabosonofmasszero?If~hiswere~ruewewouldhaveapossib

5、ilitytoestablish,e.g.,thephotonina(1)H.P.DT2RRandH.WINTER:~UOVOCimento,70A,467(1970).4O4GA]JG]~INVARIANCEAN]:)MASSLESSGAUGEPARTICL]~SINSPINORTHEORY~0~spinortheoryasagaugepaI~icleconnectedwiththegaugetransformationy~(x)~-~exp[i~(x)l~2~]W(x).Itprovespossible--atleastin~firstappro

6、ximation--toshowtheexistenceofmasslessbosonsconnectedwiththegaugetransformation.Atfirstwehavetodefinethelocalproductofthreespinorfieldsinsuchawayastogetcon-sistencywiththeansatzforthefermionpropagator(Sect.1).Thenwehavetotakethecorrec~valueforthecouplingconstanttoguaranteegauge

7、inva-riance(Sect.2).Theseconditionsyieldwell-definedbosonequationswithmasslessbosonsconnectedwiththegaugetransformation(Sect.3).l.-Redefinitionofthespinorequation.Wewritedownthespinorequationintheform(1.1)(i~+z)~(x)÷:V~w(~V,~):(x)=oandweshallassumetheFasaspinorpotentiM(1,2).The

8、physicalfieldsZariseonlyafterderivationorbytakingcaref