Chaichian2001-Path Integrals in Physics， vol.I. Stochastic Process &ampamp;amp; Quantum Mechanics.pdf

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1、PathIntegralsinPhysicsVolumeIStochasticProcessesandQuantumMechanicsPathIntegralsinPhysicsVolumeIStochasticProcessesandQuantumMechanicsMChaichianDepartmentofPhysics,UniversityofHelsinkiandHelsinkiInstituteofPhysics,FinlandandADemichevInstituteofNuclearPhysics,MoscowStateUniversity,Russ

2、iaInstituteofPhysicsPublishingBristolandPhiladelphia
cIOPPublishingLtd2001Allrightsreserved.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,UKUSOf?ce: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