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1、PHYSICALREVIEWDVOLUME36,NUMBER615SEPTEMBER1987NewHamiltonianformulationofgeneralrelativityAbhayAshtekarPhysicsDepartment,SyracuseUniversity,Syracuse,NewYork13244-1130andInstituteofTheoreticalPhysics,UniversityofCalifornia,SantaBarbara,California93106andMaxPlan-ck
2、Insti-tutfurAstrophysik,D8046G-arching,FederalRepublicofGermany(Received5December1986)Thephasespaceofgeneralrelativityisfirstextendedinastandardmannertoincorporatespi-nors.Newcoordinatesarethenintroducedonthisenlargedphasespacetosimplifythestructureofconstrainteq
3、uations.Now,thebasicvariables,satisfyingthecanonicalPoisson-bracketsrela-tions,arethe(density-valued)solderingforms0.'&andcertainspin-connectionone-formsA,&ConstraintsofEinstein'stheorysimplystatethato.'satisfiestheGausslawconstraintwithrespecttoA,andthatthecurva
4、turetensorF,»andA,satisfiescertainpurelyalgebraicconditions(in-'volvingo.').Inparticular,theconstraintsareatworstquadraticinthenewvariableso.andA,.Thisisinstrikingcontrastwiththesituationwithtraditionalvariables,whereconstraintscontainnonpolynomialfunctionsofthet
5、hree-metric.SimplificationoccursbecauseA,hasinformationaboutboththethree-metricanditsconjugatemomentum.Inthefour-dimensionalspace-timepic-ture,A,turnsouttobeapotentialfortheself-dualpartofWeylcurvature.Animportantfeatureofthenewformofconstraintsisthatitprovidesan
6、aturalembeddingoftheconstraintsurfaceoftheEinsteinphasespaceintothatofYang-Millsphasespace.Thisembeddingprovidesnewtoolstoanalyzeanumberofissuesinbothclassicalandquantumgravity.Someillustrativeapplica-tionsarediscussed.Finally,the(Poisson-bracket)algebraofnewcons
7、traintsiscomputed.Theframeworksetsthestageforanotherapproachtocanonicalquantumgravity,discussedinforth-comingpapersalsobyJacobson,Lee,Renteln,andSmolin.I.INTRODUCTIONform.ThepurposeofthispaperistointroducenewvariablesonthegravitationalphasespacewhichbringTheprese
8、nceofgaugefreedominaphysicaltheoryaboutsuchasimplification.Furthermore,theuseofrejectsitselfinitsHamiltonianformulationthroughthethesevariablesenablesonetoembe
