Feynman-Diagram

Feynman-Diagram

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时间:2019-07-04

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1、Feynmandiagram1FeynmandiagramFeynmandiagramsareapictorialrepresentationschemeforthemathematicalexpressionsgoverningthebehaviorofsubatomicparticles.Thecalculationofprobabilityamplitudesintheoreticalparticlephysicsrequirestheuseofsomeratherlargeandcomplicatedintegralsoveralargenumberofvariables.The

2、seintegralsdo,however,havearegularstructure,andmayberepresentedgraphicallyasFeynmandiagrams.AFeynmandiagramallowsforasimplevisualizationofwhatwouldotherwisebearatherarcaneandabstractformula.InthisFeynmandiagram,anelectronandapositronannihilate,producingavirtualphotonthatbecomesaquark-antiquarkpai

3、r.Thenoneradiatesagluon.Moreprecisely,aFeynmandiagramisagraphicalrepresentationofaperturbativecontributiontothetransitionamplitudeorcorrelationfunctionofaquantummechanicalorstatisticalfieldtheory.WithinthecanonicalformulationofquantumfieldtheoryaFeynmandiagramrepresentsatermintheWick'sexpansionof

4、theperturbativeS-matrix.Alternatively,thepathintegralformulationofquantumfieldtheoryrepresentsthetransitionamplitudeasaweightedsumofallpossiblehistoriesofthesystemfromtheinitialtothefinalstate,intermsofeitherparticlesorfields.AFeynmandiagramisthenacontributionofaparticularclassofparticlepaths,whi

5、chjoinandsplitasdescribedbythediagram.ThetransitionamplitudeisthengivenasthematrixelementoftheS-matrixbetweentheinitialandthefinalstatesofthequantumsystem.FeynmandiagramsweredevelopedbyRichardFeynman,andarenamedafterhim.Therearemanyapplications,primarilyinquantumfieldtheory,butalsoinotherfields,e

6、.g.,insolid-statetheory.MotivationandhistoryWhencalculatingscatteringcrosssectionsinparticlephysics,theinteractionbetweenparticlescanbedescribedbystartingfromafreefieldwhichdescribestheincomingandoutgoingparticles,andincludinganinteractionHamiltoniantodescribehowtheparticlesdeflectoneanother.Thea

7、mplitudeforscatteringisthesumofeachpossibleinteractionhistoryoverallpossibleInthisdiagram,akaon,madeofanupandanti-strangequark,decaysbothweaklyintermediateparticlestates.Thenumberofandstronglyintothreepions,withinterme

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