an introduction to quantum field theory - peskin and schroeder

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1、PartIFeynmanDiagramsandQuantumElectrodynamicsChapter1Invitation:PairProduction+;ineeAnnihilationThemainpurposeofPartIofthisbookistodevelopthebasiccalculationalmethodofquantumeldtheory,theformalismofFeynmandiagrams.WewillthenapplythisformalismtocomputationsinQuantumElectrodynamics,thequantumtheor

2、yofelectronsandphotons.QuantumElectrodynamics(QED)isperhapsthebestfundamentalphys-icaltheorywehave.Thetheoryisformulatedasasetofsimpleequations(Maxwell'sequationsandtheDiracequation)whoseformisessentiallydeter-minedbyrelativisticinvariance.Thequantum-mechanicalsolutionsoftheseequationsgivedetaile

3、dpredictionsofelectromagneticphenomenafrommacro-scopicdistancesdowntoregionsseveralhundredtimessmallerthanthepro-ton.Feynmandiagramsprovideforthiseleganttheoryanequallyelegantpro-cedureforcalculation:Imagineaprocessthatcanbecarriedoutbyelectronsandphotons,drawadiagram,andthenusethediagramtowritet

4、hemathe-maticalformofthequantum-mechanicalamplitudeforthatprocesstooccur.InthisrstpartofthebookwewilldevelopboththetheoryofQEDandthemethodofFeynmandiagramsfromthebasicprinciplesofquantummechanicsandrelativity.Eventually,wewillarriveatapointwherewecancalculateobservablequantitiesthatareofgreatint

5、erestinthestudyofele-mentaryparticles.Buttoreachourgoalofderivingthissimplecalculationalmethod,wemustrst,unfortunately,makeaseriousdetourintoformalism.Thethreechaptersthatfollowthisonearealmostcompletelyformal,andthereadermightwonder,inthecourseofthisdevelopment,wherewearego-ing.Wewouldliketopar

6、tiallyanswerthatquestioninadvancebydiscussingthephysicsofanespeciallysimpleQEDprocess

7、onesucientlysimplethatmanyofitsfeaturesfollowdirectlyfromphysicalintuition.Ofcourse,thisintuitive,bottom-upapproachwilcontainmanygaps.InChapter5wewillreturntothisprocesswiththefullpoweroftheFeynmandiagramformal

8、ism.Workingfromthetopdown,wewillthenseeallofthesedicultiessweptaway.3+;4Chapter1Invitation:PairProductionineeAnnihilation+;+;Figure1.1.Theannihilationreactionee!,showninthecenter-of-massframe.TheSimplestSituationSin