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1、LoopQuantumGravity(ReviewwrittenfortheelectronicjournalLIVINGREVIEWS)CarloRovelli,DepartmentofPhysicsandAstronomy,UniversityofPittsburgh,PittsburghPa15260,USArovelli@pitt.edu(September29,1997)AbstractTheproblemof ndingthequantumtheoryofthegravitational eld,andthusunderstandingwhatisquantumspace-
2、time,isstillopen.Oneofthemostactiveofthecurrentapproachesisloopquantumgravity.Loopquantumgravityisamathematicallywell-de ned,non-perturbativeandbackgroundindependentquantizationofgeneralrelativity,withitsconventionalmattercouplings.Theresearchinloopquantumgravityformstodayavastarea,rangingfromma
3、thematicalfoundationstophysicalapplications.Amongthemostsigni cativeresultsobtainedare:(i)Thecompu-tationofthephysicalspectraofgeometricalquantitiessuchasareaandvolume;whichyieldsquantitativepredictionsonPlanck-scalephysics.(ii)AderivationoftheBekenstein-Hawkingblackholeentropyformula.(iii)Anint
4、riguingphysicalpictureofthemicrostructureofquantumphysicalspace,characterizedbyapolymer-likePlanckscaledis-creteness.Thisdiscretenessemergesnaturallyfromthequantumtheoryandprovidesamathematicallywell-de nedrealizationofWheeler'sintuitionofaspacetimefoam".Longstandingopenproblemswithintheapproac
5、h(lackofascalarproduct,overcompletenessoftheloopbasis,implementationofrealityconditions)havebeenfullysolved.Theweakpartoftheapproachisthetreatmentofthedynamics:atpresentthereexistseveralproposals,whichareintenselydebated.Here,Iprovideageneraloverviewofideas,techniques,resultsandopenproblemsofthi
6、scandidatetheoryofquantumgravity,andaguidetotherelevantliterature.I.INTRODUCTIONingtherealityconditionsinthequantumtheory)havebeensolidlyandsatisfactorilysolved.ButwhileitisTheloopapproachtoquantumgravityistenyearsold.fairlywelldeveloped,loopquantumgravityisnotyetThe rstannouncementofthisapproac
7、hwasgivenataacompletetheory.Norhasitsconsistencywithclas-conferenceinIndiain1987[182].Thistenthanniversarysicalgeneralrelativitybeen rmlyestablishedyet.Theisagoodopportunityforattemptinganassessmentofsectorofthetheorywhichha
