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1、LoopQuantumGravityCarloRovelliDepartmentofPhysicsandAstronomyUniversityofPittsburgh,PittsburghPA15260,USArovelli@pitt.eduhttp://www.pitt.edu/~rovelliPublishedon26January1998www.livingreviews.org/Articles/Volume1/1998-1rovelliLivingReviewsinRelativityPublishedbytheMax-Planck-Institu
2、teforGravitationalPhysicsAlbertEinsteinInstitute,Potsdam,GermanyAbstractTheproblemof ndingthequantumtheoryofthegravitational eld,andthusunderstandingwhatisquantumspacetime,isstillopen.Oneofthemostactiveofthecurrentapproachesisloopquantumgravity.Loopquantumgravityisamathematicallywe
3、ll-de ned,non-perturbativeandbackgroundindependentquantizationofgeneralrelativity,withitsconventionalmattercouplings.Researchinloopquantumgravitytodayformsavastarea,rangingfrommathematicalfoundationstophysicalapplications.Amongthemostsigni cantresultsobtainedare:(i)Thecomputationof
4、thephysicalspectraofgeometricalquantitiessuchasareaandvolume,whichyieldsquantitativepredictionsonPlanck-scalephysics.(ii)AderivationoftheBekenstein-Hawkingblackholeentropyformula.(iii)Anintriguingphysicalpictureofthemicrostructureofquantumphys-icalspace,characterizedbyapolymer-like
5、Planckscalediscreteness.Thisdiscretenessemergesnaturallyfromthequantumtheoryandprovidesamathematicallywell-de nedrealizationofWheeler'sintuitionofaspace-timefoam".Longstandingopenproblemswithintheapproach(lackofascalarproduct,over-completenessoftheloopbasis,implementationofreality
6、conditions)havebeenfullysolved.Theweakpartoftheapproachisthetreatmentofthedynamics:atpresentthereexistseveralpropos-als,whichareintenselydebated.Here,Iprovideageneraloverviewofideas,techniques,resultsandopenproblemsofthiscandidatetheoryofquantumgravity,andaguidetotherelevantliterat
7、ure.c1998Max-Planck-Gesellschaftandtheauthors.Furtherinformationoncopyrightisgivenathttp://www.livingreviews.org/Info/Copyright/.Forpermissiontoreproducethearticlepleasecontactlivrev@aei-potsdam.mpg.de.ArticleAmendmentsOnauthorrequestaLivingReviewsarticlecanbeamendedtoincludeerrata
8、andsmalladditionstoensuret
