理论物理学家诺贝尔奖获得者G.t'Hooft论文.pdf

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1、~.A~.1NuclearPhysicsB44(1972)189-213.North-HollandPublishingCompanyREGULARIZATIONANDRENORMALIZATIONOFGAUGEFIELDSG.'tHOOFTandM.VELTMANInstituteforTheoreticalPhysics*,UniversityofUtrechtReceived21February1972Abstract:Anewregularizationandrenormalizationprocedureispresented.Itisparticularlywellsuitedf

2、orthetreatmentofgaugetheories.ThemethodworksfortheoriesthatwereknowntoberenormalizableaswellasforYang-Millstypetheories.Overlappingdiver-genciesaredisentangled.Theprocedurerespectsunitarity,causalityandallowsshiftsofintegrationvariables.Innon-anomalouscasesalsoWardidentitiesaresatisfiedatallstages.

3、Itistransparentwhenanomalies,suchastheBell-Jackiw-Adleranomaly,mayoccur.1.INTRODUCTIONRecentlyithasbeenshown[1]thatitispossibletoformulaterenormalizabletheoriesofchargedmassivevectorbosons.ThederivedFeynmanrulesinvolveghostparticles,andinordertoestablishunitarityandcausalityoftheS-matrixWardiden-ti

4、tiesareneeded.Thenecessarycombinatorialtechniquesweregiveninref.[2],inthetreatmentofmasslessYang-Millsfields.Itwasemphasizedthatthesesametech-niquesworkalsointhecaseofmassivevectorbosontheoriesobtainedfromthemasslesstheorybymeansoftheHiggs-Kibble[3]mechanism.Statedsomewhatdi,'-ferently:themanifestl

5、yrenormalizableset**ofFeynmanrulesinvolvingghostsmaybetransformedintoasetofmanifestlyunitaryandcausalFeynmanrulesbymeansofWardidentities.ActuallythesemanifestlyunitaryandcausalFeynmanrulesarequitemeaninglessinviewoftheoccurringdivergencies,andadirectproofofunita-ryandcausalitystartingfromthemanifes

6、tlyrenormalizablerolesistobepreferred.Thisispreciselytheprogramcarriedthroughinrefs.[1,2].However,evenwithasetofmanifestlyrenormalizablerulesonecannotbesurethataconsistenttheoryresultsunlessasuitablecut-offandsubtractionprocedurehasbeendefined.Inparticular,sinceunitaritydependscruciallyonthevalidit

7、yoftheWardindentitiesonemusthaveaprocedurethatrespectsthoseWardidentities.Inref.[2]theexistenceofsuchaprocedurewasprovenfordiagramscontainingat*Postaladdress:Maliesingel23,Utrecht,theNetherlands.**i.e.renor