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《PhysRevD.28.2960 Wave function of the Universe》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、PHYSICALREVIEWDVOLUME28,NUMBER1215DECEMBER1983WavefunctionoftheUniverseJ.B.HartleEnricoFermiInstitute,UniversityofChicago,Chicago,Illinois60637andInstituteforTheoreticalPhysics,UniversityofCalifornia,SantaBarbara,California93106S.W.HawkingDepartmentofAppliedMathematicsandTheoreticalPhy
2、sics,SilverStreet,Cambridge,EnglandandInstituteforTheoreticalPhysics,UniversityofCalifornia,SantaBarbara,California93106(Received29July1983)Thequantumstateofaspatiallycloseduniversecanbedescribedbyawavefunctionwhichisafunctionalonthegeometriesofcompactthree-manifoldsandonthevaluesofthe
3、matterfieldsonthesemanifolds.ThewavefunctionobeystheWheeler-DeWittsecond-orderfunctionaldifferentialequation.Weputforwardaproposalforthewavefunctionofthe"groundstate"orstateofminimumexcitation:theground-stateamplitudeforathree-geometryisgivenbyapathintegraloverallcompactpositive-defini
4、tefour-geometrieswhichhavethethree-geometryasaboundary.TherequirementthattheHamiltonianbeHermitianthendefinestheboundaryconditionsfortheWheeler-DeWittequationandthespectrumofpossibleexcitedstates.Toillustratetheabove,wecalculatethegroundandexcitedstatesinasimpleminisuperspacemodelinwhi
5、chthescalefactoristheonlygravitationaldegreeoffreedom,aconformallyinvariantscalarfieldistheonlymatterde-greeoffreedomandA&0.ThegroundstatecorrespondstodeSitterspaceintheclassicallimit.Thereareexcitedstateswhichrepresentuniverseswhichexpandfromzerovolume,reachamax-imumsize,andthenrecoll
6、apsebutwhichhaveafinite(thoughverysmall)probabilityoftunnelingthroughapotentialbarriertoadeSitter-typestateofcontinualexpansion.Thepath-integralap-proachallowsustohandlesituationsinwhichthetopologyofthethree-manifoldchanges.Weesti-matetheprobabilitythatthegroundstateinourminisuperspace
7、modelcontainsmorethanonecon-nectedcomponentofthespacelikesurface.I.INTRODUCTIONofpathswhichintersectxattimetandwhichareweight-edinawaythatreflectsthepreparationofthesystem.Inanyattempttoapplyquantummechanicstotheg(x,t)isthewavefunctionforthestatedeterminedbyUniverseasawholethespecifi
