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1、HUB-EP-96/30AnIntroductiontotheWorldlineTechniqueforQuantumFieldTheoryCalculationsChristianSchubertHumboldtUniversitatzuBerlinInvalidenstr.110,D-10115Berlin,Germanyschubert@qft2.physik.hu-berlin.deLecturesgivenattheXXXVICracowSchoolofTheoreticalPhysics,Zakopane,Pol
2、and,June1{10,1996.hep-th/9610108v23Aug97AbstractThesetwolecturesgiveapedagogicalintroductiontothestring-inspired"worldlinetechniqueforperturbativecalculationsinquan-tum eldtheory.Thisincludesanoverviewoverthepresentrangeofitsapplications.Severalexamplesarecalculate
3、dindetail,uptothethree-looplevel.Theemphasisisonphotonscatteringinquantumelectrodynamics.SupportedbyDeutscheForschungsgemeinschaft.IntroductionManyone-loopamplitudesinrelativisticquantum eldtheoryadmitrepresen-tationsintermsofpathintegralsoverthespaceofclosedloops[
4、1,2,3,4,5,6,7].ThosepathintegralsarecloselyrelatedtotheFeynmanpathintegralsusedinnonrelativisticquantummechanics,thoughtheyhaveperhapsnotreachedquitethesamepracticalimportance.Stillthereexistsaconsiderableamountoflit-eratureonapplicationsofparticlepathintegralstoqua
5、ntum eldtheory(seee.g.[8,9,10,11,12,13,14]),towhichIcannotpossiblydojusticehere.Thesubjectoftheselecturesratherisaspeci candnovelwayofevaluatingthistypeofpathintegral.Thismethodmaybecalledstring{inspired"becauseitisanalogoustocalculationsinstringperturbationtheory,
6、anditsdevelopmentwastriggeredbye orts[15,16]tousethepeculiarorganizationofstringamplitudestoimproveontheeciencyofcalculationsinordinaryquantum eldtheory.Howeverthisistosomeextentaccidental,andthepracticalapplicationofthistechniquerequiresnoknowledgeofstringtheory.T
7、helecturesaremeantasanintroductionforpracticionersinquantum eldtheory.Moree ortwillthereforebespentonexplainingthecalculationrulesoftheworldlineformalism,thanonrigorousderivations.The rstlectureisdevotedtothetheoreticalside.Iwill rstsketchthehistoryofthesubject,andt
8、hengiveanoverviewovertherangeofone-loopamplitudesin eldtheorywhicharepresentlyaccessibletothismethod.Iconcentratethenontheexplanationofane
