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1、LoopQuantumGravityCarloRovelliDepartmentofPhysicsandAstronomyUniversityofPittsburgh,PittsburghPA15260,USArovelli@pitt.eduhttp://www.pitt.edu/~rovelliPublishedon26January1998www.livingreviews.org/Articles/Volume1/1998-1rovelliLivingReviewsinRelativityPublishedb
2、ytheMax-Planck-InstituteforGravitationalPhysicsAlbertEinsteinInstitute,Potsdam,GermanyAbstractTheproblemof ndingthequantumtheoryofthegravitational eld,andthusunderstandingwhatisquantumspacetime,isstillopen.Oneofthemostactiveofthecurrentapproachesisloopquantumg
3、ravity.Loopquantumgravityisamathematicallywell-de ned,non-perturbativeandbackgroundindependentquantizationofgeneralrelativity,withitsconventionalmattercouplings.Researchinloopquantumgravitytodayformsavastarea,rangingfrommathematicalfoundationstophysicalapplica
4、tions.Amongthemostsigni cantresultsobtainedare:(i)Thecomputationofthephysicalspectraofgeometricalquantitiessuchasareaandvolume,whichyieldsquantitativepredictionsonPlanck-scalephysics.(ii)AderivationoftheBekenstein-Hawkingblackholeentropyformula.(iii)Anintrigui
5、ngphysicalpictureofthemicrostructureofquantumphys-icalspace,characterizedbyapolymer-likePlanckscalediscreteness.Thisdiscretenessemergesnaturallyfromthequantumtheoryandprovidesamathematicallywell-de nedrealizationofWheeler'sintuitionofaspace-timefoam".Longstan
6、dingopenproblemswithintheapproach(lackofascalarproduct,over-completenessoftheloopbasis,implementationofrealityconditions)havebeenfullysolved.Theweakpartoftheapproachisthetreatmentofthedynamics:atpresentthereexistseveralpropos-als,whichareintenselydebated.Here,
7、Iprovideageneraloverviewofideas,techniques,resultsandopenproblemsofthiscandidatetheoryofquantumgravity,andaguidetotherelevantliterature.c1998Max-Planck-Gesellschaftandtheauthors.Furtherinformationoncopyrightisgivenathttp://www.livingreviews.org/Info/Copyright/
8、.Forpermissiontoreproducethearticlepleasecontactlivrev@aei-potsdam.mpg.de.ArticleAmendmentsOnauthorrequestaLivingReviewsarticlecanbeamendedtoincludeerrataandsmalladditionstoensuret
