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1、LectureNotesonTHEORYLectureNotesonTHEORYSenHuPrincetonUniversityyeWorldScientificbSingapore.NewJersey.London'HangKongPublishedbyWorldScientificPublishingCo.Ptc.Ltd.P0Box128,FmerRoad,Singapore912805USAofice:SuiteIB,1060MainStreet,RiverEdge,NJ07661UKofice:5
2、7SheltonStreet,CoventGarden,LondonWC2H9HEBritishLibraryCataloguing-in-PublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibrary.LECTURENOTESONCHERN-SIMONS-WITTENTHEORYCopyright02001byWorldScientificPublishingCo.Pte.Ltd.Allrightsreserved.T
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5、Uto-PrintTomyparentsToBo,MaomaoandAmyPrefaceMorethan15yearsago,VaughnJonesdiscoveredanelegant,constructionofanewpolynomialinvariantforknotsinthree-dimensionalspace.Jones'sdiscoveryhasbeengeneralizedinmanydirectionsandavarietyofnewdefinitionshavebeenfound.
6、MathematicallyrigorousapproachestotheJonespolynomialanditsgeneralizationstendtobecombinatorialinnature.Thesedefinitionsoftenlackmanifestthree-dimensionalsymmetry,butthissymmetrycansome-timesbeprovedbyshowingirivariariceuriderariappropriatesetof“moves”.The
7、reisalsoanalternativeapproachtothissubject,discoveredby“physical”methodsafewyearsafterVaughnJones’sinitialwork.Inthisapproach,thebasicobjectofstudyisathree-dimensionalquantumgaugetheoryinwhichtheactionistheChern-Simonsinvariantofaconnection.Knotinvariants
8、andthree-manifoldinvariantscanbedefinedinthistheory,ataphysicallevelofrigor.UsingtheFeynmanpathintegral,thevariousinvariantscanbedescribedinawaythatmanifestthefullthree-dimensionalsymmetry.(Indeed,Feynmanoriginallyi
