资源描述：
《introduction to matrix theory and noncommutative geometry - anatoly konechny(et al)》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、IntroductiontoM(atrix)theoryandnoncommutativegeometryAnatolyKonechny1andAlbertSchwarz2y1DepartmentofPhysics,UniversityofCaliforniaBerkeleyandTheoreticalPhysicsGroup,MailStop50A-5101LBNL,Berkeley,CA94720USAkonechny@thsrv.lbl.gov2DepartmentofMathematics,Univer
2、sityofCaliforniaDavisDavis,CA95616USAschwarz@math.ucdavis.eduAugust3,2001AbstractNoncommutativegeometryisbasedonanideathatanassociativealgebracanberegardedas"analgebraoffunctionsonanoncommutativespace".ThemajorcontributiontononcommutativegeometrywasmadebyA.Co
3、nnes,who,inparticular,analyzedYang-Millstheoriesonnoncommutativespaces,usingimportantnotionsthatwereintroducedinhispapers(connection,Cherncharacter,etc).ItwasfoundrecentlythatYang-Millstheoriesonnoncommutativespacesappearnaturallyinstring/M-theory;thenotionsa
4、ndresultsofnoncommutativegeometrywereappliedverysuccessfullytotheproblemsofphysics.Inthispaperwegiveamostlyself-containedreviewofsomeaspectsofM(atrix)theory,ofConnes'noncommutativegeometryandofapplicationsofnoncommutativegeometrytoM(atrix)theory.Thetopicsincl
5、udeintroductiontoBFSSandIKKTmatrixmodels,compacti cationsonnoncommutativetori,areviewofbasicnotionsofnoncommutativegeometrywithadetaileddiscussionofnoncommutativetori,MoritaequivalenceandSO(d;djZ)-duality,anelementarydiscussionofinstantonsandnoncommutativeorb
6、ifolds.ThereviewisprimarilyintendedforphysicistswhowouldliketolearnsomebasictechniquesarXiv:hep-th/0012145v329Jul2001ofnoncommutativegeometryandhowtheycanbeappliedinstringtheoryandtomathematicianswhowouldliketolearnaboutsomenewproblemsarisingintheoreticalphys
7、ics.Contents1Introduction32Yang-Millstheoryreducedtoapoint43Matrixmodels83.1IKKTmatrixmodel...............................8ResearchsupportedbytheDirector,OceofEnergyResearch,OceofHighEnergyandNuclearPhysics,DivisionofHighEnergyPhysicsoftheU.S.DepartmentofE
8、nergyunderContractDE-AC03-76SF00098andinpartbytheNationalScienceFoundationgrantPHY-95-14797.yResearchsupportedinpartbyNSFgrantDMS-980100913.2BFSSmatrixquantummechanics....................
