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1、LoopQuantumGravityandBlackHolePhysicsCarloRovelliDepartmentofPhysicsandAstronomy,UniversityofPittsburgh,PittsburghPa15260,USAJanuary10,2002AbstractIsummarizethebasicideasandformalismofloopquantumgravity.Iillustratetheresultsonthediscreteaspectsofquantumgeometryandtwoapplica
2、tionsoftheseresultstoblackholephysics.Inparticular,IdiscussindetailthederivationoftheBekenstein-Hawkingformulafortheentropyofablackholefrom rstprinciples.1IntroductionThelackofunderstandingofthequantumbehaviorofthegravitational eld,andthereforethelackofunderstandingofquantum
3、geometry,remainsama-joropenprobleminfundamentalphysics.Therearetentativetheorieswhicharepresentlyintensivelyinvestigated.Forinstance,thereisperturbativestringtheory,andnon-perturbativestringtheory,muchstudiedinthesedays.1AlessarXiv:gr-qc/9608032v114Aug1996ambitiousattempttos
4、olvetheproblemisnonperturbativequantumgravity,orloopquantumgravity".2Thisistheprojectoftakingtheconceptualnov-eltiesintroducedinphysicsbygeneralrelativityveryseriously,andtryingtomakesenseofquantumgeneralrelativity(oranyotherhighenergyextensionofgeneralrelativity)nonperturb
5、atively.TheprogramisbasedonthehypothesisthatperturbativeapproachesfailtodescribePlanckscalephysicsbecauseatthePlanckscaletheseparationbe-tweenabackgroundmetricandaquantum eldisnotphysicallyjusti ed.Atshortscale,spacetimeisnotMinkoskian.Aposteriori,loopquantumgravitysupportst
6、hehypothesis,sincetheshortstructureofthegeometryturnsoutE-mail:rovelli@pitt.edu1Foranoverviewofothercurrentideasonquantumgeometry,see[1],[2],and[3]2TedJacobsoncallsitLoopyquantumgravity".1tobestronglynon-Minkoskianinthenonperturbativetheory[4].Thus,Manshallnotseparatewhat
7、Einsteinputtogether":weshouldnotseparatethegrav-itational eldfromthemetric.Ifthisideaiscorrect,thenthequantumgravitational eldcannotbede-scribedasaquantum eldoverametricmanifold,becausethereisnoback-ground eldtoprovidethemetricstructure.Thereforewehavetolearnhowtoconstructaq
8、uantum eldtheorylivingoverastructureweakerthanamet-ricmanifold:namelyoverad
