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1、REVIEWSOFMODERNPHYSICSVOLUME20,NUMHER1JANUARY,1948AGenera..izei'..'.xeoryoIGravitationALBERTEINSTEINInstituteforAdvancedStudy,Princeton,NewJersey''Nthefollowingweshallgiveanewpresenta-ofrank2,tionofthegeneralizedtheoryofgravitation,gg,——QcA„Ai„whichconstitutesacertainprogressinclarityasc
2、omparedtothepreviouspresentations.*Itiswherethecareagainrealconstants.ouraimtoachieveatheoryofthetotalfieldbyaThedeterminantg=Ig,sI(WO)isreal.generalizationoftheconceptsandmethodsofProof:therelativistictheoryofgravitation.la'.I=la"I=la'.I=li'~li.THEFIELDSTRUCTUREWecanassociateacontravari
3、antg'totheThetheoryofgravitationrepresentsthefieldcovariantg;kjustasinthecaseofrealfieldsbybyasymmetrictensorg;~,i.e.,g;q=gq;(i,k=&,setting~~,4),wheretheg,tarerealfunctionsofXgp'''X4a.a'=&"(ora.r"=~')InthegeneralizedtheorythetotalfieldisrepresentedbyaHermitiantensor.Thesym-wherebistheKro
4、neckertensor.Heretheordermetrypropertyofthe(complex)g;&isofindicesisimportantand,forexample,g;,g"doesnotequal8.Inthefollowingthetensorgikgki&~densityg'"=g's(g)playsanimportantrole.FromagrouptheoreticalpointofviewtheIfwedecomposeg,&intoitsrealandimaginaryintroductionofaHermitiantensorisso
5、mewhatcomponents,thentheformerisasymmetricarbitrary,sincebothindividualadditivecom-tensor(g;&),thelatteranantisymmetrictensorponentsgkandg@havetensorcharacter.(gp).Theg;sarestillfunctionsoftherealHowever,thisflawissomewhatamelioratedbyvariablesx~,.~,x4.thefactthat,justasinthecaseofrealfi
6、elds,Theformallynaturalcharacterofthisgeneral-thereisanaturalwayofassociatingparallelizationofthesymmetrictensorbecomespar-translationstotheHermitiangg„thisisthemainticularlynoticeablebythefollowingconsidera-basisforthec1aimthattheintroductionofation:FromthecovariantvectorA;onecanformHer
7、mitiangg,isnatural.throughmultiplicationtheparticularsymmetriccovarianttensorA&s.Fromsuchtensorsevery2.INFINITESIMALPARALLELTRANSLATIONS,symmetrictensorofrank2canbeobtainedABSOLUTEDIFFERENTIATIONANDCURVATUREthroughsummationwithrealcoefficients:Inthetheoryofrealfieldswegiv
