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1、IntroductiontoModernCanonicalQuantumGeneralRelativityT.Thiemann1MPIf.Gravitationsphysik,Albert-Einstein-Institut,AmMuhlen•berg1,14476GolmnearPotsdam,GermanyPreprintAEI-2001-119arXiv:gr-qc/0110034v15Oct20011thiemann@aei.mpg.deAbstractThisisanintroductiontothebynow fteeny
2、earsoldresearch eldofcanonicalquantumgeneralrelativity,sometimescalledloopquantumgravity".Thetermmodern"inthetitlereferstothefactthatthequantumtheoryisbasedonformulatingclassicalgeneralrelativityasatheoryofconnectionsratherthanmetricsascomparedtoinoriginalversiondueto
3、Arnowitt,DeserandMisner.Canonicalquantumgeneralrelativityisanattempttode neamathematicallyrigorous,non-perturbative,backgroundindependenttheoryofLorentzianquantumgravityinfourspacetimedi-mensionsinthecontinuum.Assuchitdi ersconsiderablyfromperturbativeans•atze.Itprovide
4、sauni edtheoryofallinteractionsinthesensethatallinteractionstransformunderacommongaugegroup:Thefour-dimensionaldi eomorphismgroupoftheunderlyingdi erentalmanifoldwhichismaximallybrokeninperturbativeapproaches.Theapproachisminimalinthatonesimplyana-lyzesthelogicalconsequ
5、encesofcombiningtheprinciplesofgeneralrelativitywiththeprinciplesofquantummechanics.Asaconsequence,noextradimensions,nocorrespondingKaluza-Kleincompacti cations,nosupersymmetryanditsassociatedphenomenology{compatiblespontaneousbreakingatlowenergies,seemtobenecessary.Ont
6、heotherhand,noexplanationfortheparticlecontentandthedimensionoftheuniverseisprovidedbythetheory.Therequirementtopreservebackgroundindependencehasleadtonew,fascinatingmathematicalstructureswhichonedoesnotseeinperturbativeapproaches,e.g.afundamentaldiscretenessofspacetime
7、seemstobeapredictionofthetheorywhichisa rstsubstantialevidenceforatheoryinwhichthegravitational eldactsasanaturalUVcut-o .Ane orthasbeenmadetoprovideaself-containedexpositionattheappropriatelevelofrigourwhichatthesametimeisaccessibletograduatestudentswithonlybasicknowle
8、dgeofgeneralrelativityandquantum eldtheoryonMinkowskispace.Tobeuseful,notallfacetsofthe eldhavebeencovered,how
