hu,lecture notes on chern-simons-witten theory

hu,lecture notes on chern-simons-witten theory

ID:31463112

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时间:2019-01-10

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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

3、hisbookorpartsthereof;maynotbereproducedinanyformorbyanymeans,electronicormechanical,includingphotocopying,recordingoranyinformationstorageandretrievalsystemnowknownortobeinvented,withoutwrittenpermissionfromthePublisher.Forphotocopyingofmaterialinthisvol

4、ume,pleasepayacopyingfeethroughtheCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,USA.Inthiscasepermissiontophotocopyisnotrequiredfromthepublisher.ISBN981-02-3908-4ISBN981-02-3909-2(pbk)Thisbookisprintedonacid-freepaper.PrintedinSingaporeby

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

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