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1、—DRAFT—IASSNS-HEP-97/72LectureIPointParticlesvsStringsEricD’HokerInphysics,thestructureofmatterisunderstoodintermsofthedynamicsofsmallerconstitutents.Atomsarecomposedofnucleiandelectrons,nucleiaremadeupofpro-tonsandneutrons,whichinturnareboundstatesofquarks.Tothep
2、resentdaylimitofdistancescalesuptoapproximately10−15cm,electronsandquarksdonotshowanysubstructure,andareviewedas“elementaryparticles”.(Whichparticlesareelementaryinthiswaymaychangeovertime,sinceatsmallerdistancescalessubstructuremaybefoundintermsofmoreelementarypa
3、rticles.)Inquantumfieldtheory,suchelementaryparticlesaredescribedaspointsinspace.Forcesbetweenparticlesresultfromexchangesbetweenthemofotherelementaryparticles,andthefundamentalinteractionsoccurinalocalway,atcoincidenttimeatthesamepointinspace.Forexampleelectro-mag
4、neticinteractionforcesbetweenchargedparticlesresultfromtheexchangeofphotons,withlocalcouplingstothechargedparticles.Thephotontherebytransfersmomentumandproducesaforce,theCoulombforce.Quantumfieldtheoryofpointparticles(QFT)hasbeenextremelysuccessfulinde-scribingquan
5、titativelythreeoutofthefourfundamentalforcesofNaturebyYang-Millstheory:electro-magnetic,weakandstronginteractions.However,noconsistentquantumI.1fieldtheorydescriptionappearstobeavailable(ortoexist?)fortheforceofgravity.OnethusseeksanenlargementoftheframeworkofQFTin
6、whichallforcesofnaturefitconsis-tentlywiththeknownphysicalprinciplesofquantummechanicsand(specialandgeneral)relativity.Stringtheorytodateseemstobetheonlysuchcandidate.Infactmytaskwillbetoshowthatconsistentstringtheoriesautomaticallycontaingravity,supersymmetryandun
7、dercertaincircumstancesYang-Mills.A.StringsInstringtheory,particlesarenotdescribedaspoints,butinsteadasstrings:one-dimensionalextendedobjects.IfMsandM(∼R×Ms)denotethespaceandspace-timemanifoldsrespectively,thenwepicturestringsasfollows:Whilethepointparticlesweepso
8、utaone-dimensionalworldline,thestringsweepsoutaworldsheet,i.e.a2-dimrealsurface.Forafreestring,thetopologyoftheworldsheetisacylinder(inthecaseofacloseds
