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1、PathIntegralsinPhysicsVolumeIStochasticProcessesandQuantumMechanicsPathIntegralsinPhysicsVolumeIStochasticProcessesandQuantumMechanicsMChaichianDepartmentofPhysics,UniversityofHelsinkiandHelsinkiInstituteofPhysics,FinlandandADemichevInstituteofNuclearPhysics,MoscowStateUniversity,RussiaInstitut
2、eofPhysicsPublishingBristolandPhiladelphiacIOPPublishingLtd2001Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,withoutthepriorpermissionofthepublisher.Multiplecopyingispe
3、rmittedinaccordancewiththetermsoflicencesissuedbytheCopyrightLicensingAgencyunderthetermsofitsagreementwiththeCommitteeofVice-ChancellorsandPrincipals.BritishLibraryCataloguing-in-PublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibrary.ISBN075030801X(Vol.I)0750308028(Vol.II)0
4、750307137(2Vol.set)LibraryofCongressCataloging-in-PublicationDataareavailableCommissioningEditor:JamesRevillProductionEditor:SimonLaurensonProductionControl:SarahPlentyCoverDesign:VictoriaLeBillonMarketingExecutive:ColinFentonPublishedbyInstituteofPhysicsPublishing,whollyownedbyTheInstituteofPh
5、ysics,LondonInstituteofPhysicsPublishing,DiracHouse,TempleBack,BristolBS16BE,UKUSOffice:InstituteofPhysicsPublishing,ThePublicLedgerBuilding,Suite1035,150SouthIndependenceMallWest,Philadelphia,PA19106,USATypesetinTEXusingtheIOPBookmakerMacrosPrintedintheUKbyBookcraft,MidsomerNorton,BathFatehasim
6、poseduponourwritingthistometheyokeofaforeigntongueinwhichwewerenotsunglullabies.FreelyadaptedfromHermannWeylContentsPrefaceixIntroduction1Notationalconventions91Pathintegralsinclassicaltheory121.1Brownianmotion:introductiontotheconceptofpathintegration121.1.1Brownianmotionofafreeparticle,diffus
7、ionequationandMarkovchain121.1.2Wiener’streatmentofBrownianmotion:Wienerpathintegrals221.1.3Wiener’stheoremandtheintegrationoffunctionals291.1.4Methodsandexamplesforthecalculationofpathintegrals361.1.5Changeofvariablesinpathintegr
