PhysRev.76.790 Quantum Electrodynamics. III. The Electromagnetic Properties of the Electron—Radiative Corrections to Scattering

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1、PHVSICALREVIEWVOLUME76,NUMBER6SEPTEMHER15,l&49QuantumElectrodynamics.—III.TheElectromagneticPropertiesoftheElectronRadiativeCorrectionstoScatteringJULIANSCHWINGERHarvardUniversity,Cambridge,Massachusetts(ReceivedMay26,1949)Thediscussionofvacuumpolarizationinthepreviouspaperoperator,asmodi6edbyt

2、heinteractionwiththevacuumelectro-ofthisserieswascon6nedtothatproducedbythe6eldofapre-magnetic6eld.Applicationismadetothescatteringofanelectronscribedcurrentdistribution.Wenowconsidertheinductionofbyanexternalfield,inwhichthelatterisregardedasasmallcurrentinthevacuumbyanelectron,whichisadynamic

3、alsys-perturbation.ItisfoundconvenienttocalculatethetotalrateattemandanentityindistinguishablefromtheparticlesassociatedwhichcollisionsoccurandthenidentifythecrosssectionsforwithvacuumBuctuations.Theadditionalcurrentthusattributedindividualevents.Thecorrectiontothecrosssectionforradia-toanelect

4、ronimpliesanalterationinitselectromagneticproper-tionlessscatteringisdeterminedbythesecond-ordercorrectiontieswhichwillberevealedbyscatteringinaCoulomb6eldandtothecurrentoperator,whilescatteringthatisaccompaniedbybyenergyleveldisplacements.Thispaperisconcernedwiththesinglequantumemissionisacons

5、equenceofthe6rst-ordercurrentcomputationofthesecond-ordercorrectionstothecurrentopera-correction.The6nalobjectofcalculationisthediGerentialcrosstorandtheapplicationtoelectronscattering.Radiativecorrec-sectionforscatteringthroughagivenanglewithaprescribedtionstoenergylevelswillbetreatedinthenext

6、paperoftheseries.maximumenergyloss,whichiscompletelyfreeofdivergences.FollowingacanonicaltransformationwhicheGectivelyrenor-Detailedevaluationsaregivenintwosituations,theessentiallymalizestheelectronmass,thecorrectiontothecurrentoperatorelasticscatteringofanelectron,inwhichonlyasmallfractionpro

7、ducedbythecouplingwiththeelectromagneticfieldisde-ofthekineticenergyisradiated,andthescatteringofaslowlyvelopedinapowerseries,ofwhich6rst-andsecond-ordertermsmovingelectronwithunrestrictedenergyloss.TheAppendixisareretained.Onethu