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1、PathIntegralsinPhysicsVolumeIStochasticProcessesandQuantumMechanicsPathIntegralsinPhysicsVolumeIStochasticProcessesandQuantumMechanicsMChaichianDepartmentofPhysics,UniversityofHelsinkiandHelsinkiInstituteofPhysics,FinlandandADemichevInstituteofNuclearPhysics,MoscowStateUniversity,Russ
2、iaInstituteofPhysicsPublishingBristolandPhiladelphiacIOPPublishingLtd2001Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,withoutthepriorpermissionofthepublisher
3、.MultiplecopyingispermittedinaccordancewiththetermsoflicencesissuedbytheCopyrightLicensingAgencyunderthetermsofitsagreementwiththeCommitteeofVice-ChancellorsandPrincipals.BritishLibraryCataloguing-in-PublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibrary.ISBN075030
4、801X(Vol.I)0750308028(Vol.II)0750307137(2Vol.set)LibraryofCongressCataloging-in-PublicationDataareavailableCommissioningEditor:JamesRevillProductionEditor:SimonLaurensonProductionControl:SarahPlentyCoverDesign:VictoriaLeBillonMarketingExecutive:ColinFentonPublishedbyInstituteofPhysics
5、Publishing,whollyownedbyTheInstituteofPhysics,LondonInstituteofPhysicsPublishing,DiracHouse,TempleBack,BristolBS16BE,UKUSOffice:InstituteofPhysicsPublishing,ThePublicLedgerBuilding,Suite1035,150SouthIndependenceMallWest,Philadelphia,PA19106,USATypesetinTEXusingtheIOPBookmakerMacrosPrin
6、tedintheUKbyBookcraft,MidsomerNorton,BathFatehasimposeduponourwritingthistometheyokeofaforeigntongueinwhichwewerenotsunglullabies.FreelyadaptedfromHermannWeylContentsPrefaceixIntroduction1Notationalconventions91Pathintegralsinclassicaltheory121.1Brownianmotion:introductiontotheconcept
7、ofpathintegration121.1.1Brownianmotionofafreeparticle,diffusionequationandMarkovchain121.1.2Wiener’streatmentofBrownianmotion:Wienerpathintegrals221.1.3Wiener’stheoremandtheintegrationoffunctionals291.1.4Methodsandexamplesforthecalculationofpathintegrals361.1.5Changeofvariablesinpathi
8、ntegr
