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1、LoopQuantumGravity(ReviewwrittenfortheelectronicjournalLIVINGREVIEWS)CarloRovelli,DepartmentofPhysicsandAstronomy,UniversityofPittsburgh,PittsburghPa15260,USArovelli@pitt.edu(September29,1997)AbstractTheproblemof ndingthequantumtheoryofthegravitational eld,andth
2、usunderstandingwhatisquantumspace-time,isstillopen.Oneofthemostactiveofthecurrentapproachesisloopquantumgravity.Loopquantumgravityisamathematicallywell-de ned,non-perturbativeandbackgroundindependentquantizationofgeneralrelativity,withitsconventionalmattercoupli
3、ngs.Theresearchinloopquantumgravityformstodayavastarea,rangingfrommathematicalfoundationstophysicalapplications.Amongthemostsigni cativeresultsobtainedare:(i)Thecompu-tationofthephysicalspectraofgeometricalquantitiessuchasareaandvolume;whichyieldsquantitativepre
4、dictionsonPlanck-scalephysics.(ii)AderivationoftheBekenstein-Hawkingblackholeentropyformula.(iii)Anintriguingphysicalpictureofthemicrostructureofquantumphysicalspace,characterizedbyapolymer-likePlanckscaledis-creteness.Thisdiscretenessemergesnaturallyfromthequan
5、tumtheoryandprovidesamathematicallywell-de nedrealizationofWheeler'sintuitionofaspacetimefoam".Longstandingopenproblemswithintheapproach(lackofascalarproduct,overcompletenessoftheloopbasis,implementationofrealityconditions)havebeenfullysolved.Theweakpartoftheap
6、proachisthetreatmentofthedynamics:atpresentthereexistseveralproposals,whichareintenselydebated.Here,Iprovideageneraloverviewofideas,techniques,resultsandopenproblemsofthiscandidatetheoryofquantumgravity,andaguidetotherelevantliterature.I.INTRODUCTIONingtherealit
7、yconditionsinthequantumtheory)havebeensolidlyandsatisfactorilysolved.ButwhileitisTheloopapproachtoquantumgravityistenyearsold.fairlywelldeveloped,loopquantumgravityisnotyetThe rstannouncementofthisapproachwasgivenataacompletetheory.Norhasitsconsistencywithclas-c
8、onferenceinIndiain1987[182].Thistenthanniversarysicalgeneralrelativitybeen rmlyestablishedyet.Theisagoodopportunityforattemptinganassessmentofsectorofthetheorywhichha
