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1、IntroductiontoModernCanonicalQuantumGeneralRelativityT.Thiemann1MPIf.Gravitationsphysik,Albert-Einstein-Institut,AmMuhlen•berg1,14476GolmnearPotsdam,GermanyPreprintAEI-2001-119arXiv:gr-qc/0110034v15Oct20011thiemann@aei.mpg.deAbstractThisisanintroductiontothebynow fteenyearsold
2、research eldofcanonicalquantumgeneralrelativity,sometimescalledloopquantumgravity".Thetermmodern"inthetitlereferstothefactthatthequantumtheoryisbasedonformulatingclassicalgeneralrelativityasatheoryofconnectionsratherthanmetricsascomparedtoinoriginalversionduetoArnowitt,Deser
3、andMisner.Canonicalquantumgeneralrelativityisanattempttode neamathematicallyrigorous,non-perturbative,backgroundindependenttheoryofLorentzianquantumgravityinfourspacetimedi-mensionsinthecontinuum.Assuchitdi ersconsiderablyfromperturbativeans•atze.Itprovidesauni edtheoryofallin
4、teractionsinthesensethatallinteractionstransformunderacommongaugegroup:Thefour-dimensionaldi eomorphismgroupoftheunderlyingdi erentalmanifoldwhichismaximallybrokeninperturbativeapproaches.Theapproachisminimalinthatonesimplyana-lyzesthelogicalconsequencesofcombiningtheprinciple
5、sofgeneralrelativitywiththeprinciplesofquantummechanics.Asaconsequence,noextradimensions,nocorrespondingKaluza-Kleincompacti cations,nosupersymmetryanditsassociatedphenomenology{compatiblespontaneousbreakingatlowenergies,seemtobenecessary.Ontheotherhand,noexplanationforthepart
6、iclecontentandthedimensionoftheuniverseisprovidedbythetheory.Therequirementtopreservebackgroundindependencehasleadtonew,fascinatingmathematicalstructureswhichonedoesnotseeinperturbativeapproaches,e.g.afundamentaldiscretenessofspacetimeseemstobeapredictionofthetheorywhichisa rs
7、tsubstantialevidenceforatheoryinwhichthegravitational eldactsasanaturalUVcut-o .Ane orthasbeenmadetoprovideaself-containedexpositionattheappropriatelevelofrigourwhichatthesametimeisaccessibletograduatestudentswithonlybasicknowledgeofgeneralrelativityandquantum eldtheoryonMinko
8、wskispace.Tobeuseful,notallfacetsofthe eldhavebeencovered,how
