资源描述：
《an introduction to conformal field theory》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、DAMTP-1999-143REVIEWARTICLEAnIntroductiontoConformalFieldTheoryMatthiasRGaberdielzDepartmentofAppliedMathematicsandTheoreticalPhysics,SilverStreet,Cambridge,CB39EW,UKandFitzwilliamCollege,Cambridge,CB30DG,UKAbstract.Acomprehensiveintroductiontotwo-dimensionalc
2、onformal eldtheoryisgiven.PACSnumbers:11.25.HfSubmittedto:Rep.Prog.Phys.arXiv:hep-th/9910156v21Nov1999zEmail:M.R.Gaberdiel@damtp.cam.ac.ukConformalFieldTheory21.IntroductionConformal eldtheorieshavebeenatthecentreofmuchattentionduringthelast fteenyearssincethe
3、yarerelevantforatleastthreedi erentareasofmoderntheoreticalphysics:conformal eldtheoriesprovidetoymodelsforgenuinelyinteractingquantum eldtheories,theydescribetwo-dimensionalcriticalphenomena,andtheyplayacentralr^oleinstringtheory,atpresentthemostpromisingcand
4、idateforaunifyingtheoryofallforces.Conformal eldtheorieshavealsohadamajorimpactonvariousaspectsofmodernmathematics,inparticularthetheoryofvertexoperatoralgebrasandBorcherdsalgebras, nitegroups,numbertheoryandlow-dimensionaltopology.Fromanabstractpointofview,co
5、nformal eldtheoriesareEuclideanquantum eldtheoriesthatarecharacterisedbythepropertythattheirsymmetrygroupcontains,inadditiontotheEuclideansymmetries,localconformaltransformations,i.e.transformationsthatpreserveanglesbutnotlengths.Thelocalconformalsymmetryisofs
6、pecialimportanceintwodimensionssincethecorrespondingsymmetryalgebraisin nite-dimensionalinthiscase.Asaconsequence,two-dimensionalconformal eldtheorieshaveanin nitenumberofconservedquantities,andarecompletelysolvablebysymmetryconsiderationsalone.Asabona dequant
7、um eldtheory,therequirementofconformalinvarianceisveryrestrictive.Inparticular,sincethetheoryisscaleinvariant,allparticle-likeexcitationsofthetheoryarenecessarilymassless.Thismightbeseenasastrongargumentagainstanypossiblephysicalrelevanceofsuchtheories.However
8、,allparticlesofany(two-dimensional)quantum eldtheoryareapproximatelymasslessinthelimitofhighenergy,andmanystructuralfeaturesofquantum eldtheoriesarebelievedtobeunchangedinthisappro
