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1、LoopQuantumGravityandBlackHolePhysicsCarloRovelliDepartmentofPhysicsandAstronomy,UniversityofPittsburgh,PittsburghPa15260,USAJanuary10,2002AbstractIsummarizethebasicideasandformalismofloopquantumgravity.Iillustratetheresultsonthediscreteaspectsofquantumgeometryandtwoappl
2、icationsoftheseresultstoblackholephysics.Inparticular,IdiscussindetailthederivationoftheBekenstein-Hawkingformulafortheentropyofablackholefrom rstprinciples.1IntroductionThelackofunderstandingofthequantumbehaviorofthegravitational eld,andthereforethelackofunderstandingofq
3、uantumgeometry,remainsama-joropenprobleminfundamentalphysics.Therearetentativetheorieswhicharepresentlyintensivelyinvestigated.Forinstance,thereisperturbativestringtheory,andnon-perturbativestringtheory,muchstudiedinthesedays.1AlessarXiv:gr-qc/9608032v114Aug1996ambitiousa
4、ttempttosolvetheproblemisnonperturbativequantumgravity,orloopquantumgravity".2Thisistheprojectoftakingtheconceptualnov-eltiesintroducedinphysicsbygeneralrelativityveryseriously,andtryingtomakesenseofquantumgeneralrelativity(oranyotherhighenergyextensionofgeneralrelativit
5、y)nonperturbatively.TheprogramisbasedonthehypothesisthatperturbativeapproachesfailtodescribePlanckscalephysicsbecauseatthePlanckscaletheseparationbe-tweenabackgroundmetricandaquantum eldisnotphysicallyjusti ed.Atshortscale,spacetimeisnotMinkoskian.Aposteriori,loopquantumg
6、ravitysupportsthehypothesis,sincetheshortstructureofthegeometryturnsoutE-mail:rovelli@pitt.edu1Foranoverviewofothercurrentideasonquantumgeometry,see[1],[2],and[3]2TedJacobsoncallsitLoopyquantumgravity".1tobestronglynon-Minkoskianinthenonperturbativetheory[4].Thus,Mansh
7、allnotseparatewhatEinsteinputtogether":weshouldnotseparatethegrav-itational eldfromthemetric.Ifthisideaiscorrect,thenthequantumgravitational eldcannotbede-scribedasaquantum eldoverametricmanifold,becausethereisnoback-ground eldtoprovidethemetricstructure.Thereforewehaveto
8、learnhowtoconstructaquantum eldtheorylivingoverastructureweakerthanamet-ricmanifold:namelyoverad
