string theory by Kostas

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1、PreprinttypesetinJHEPstyle-PAPERVERSIONRevisedMay6,2011AnIntroductiontoStringTheoryKevinWrayAbstract:Thissetofnotesisbasedonthecourse“IntroductiontoStringTheory”whichwastaughtbyProf.KostasSkenderisinthespringof2009attheUniversityofAmsterdam.WehavealsodrawnonsomeideasfromthebooksStringTheoryandM-Th

2、eory(Becker,BeckerandSchwarz),IntroductiontoStringTheory(Polchinski),StringTheoryinaNutshell(McMahon)andSuperstringTheory(Green,SchwarzandWitten),alongwiththelecturenotesofDavidTong,sometimesword-for-word.Contents1.Introduction/Overview51.1MotivationforStringTheory51.2WhatisStringTheory81.2.1Types

3、ofStringTheories81.3OutlineoftheManuscript92.TheBosonicStringAction112.1ClassicalActionforPointParticles112.2ClassicalActionforRelativisticPointParticles122.2.1ReparametrizationInvarianceofS˜0162.2.2CanonicalMomenta182.2.3VaryingS˜0inanArbitraryBackground(GeodesicEquation)192.3Generalizationtop-Br

4、anes192.3.1TheStringAction202.4Exercises243.SymmetriesandFieldEquationsoftheBosonicString263.1GlobalSymmetriesoftheBosonicStringTheoryWorldsheet263.2LocalSymmetriesoftheBosonicStringTheoryWorldsheet303.3FieldEquationsforthePolyakovAction333.4SolvingtheFieldEquations363.5Exercises424.Symmetries(Rev

5、isited)andCanonicalQuantization454.1Noether’sMethodforGeneratingConservedQuantities454.2TheHamiltonianandEnergy-MomentumTensor484.3ClassicalMassFormulaforaBosonicString514.4WittAlgebra(ClassicalVirasoroAlgebra)524.5CanonicalQuantizationoftheBosonicString544.6VirasoroAlgebra564.7PhysicalStates584.8

6、Exercises62–1–5.RemovingGhostStatesandLight-ConeQuantization645.1SpuriousStates655.2RemovingtheNegativeNormPhysicalStates685.3Light-ConeGaugeQuantizationoftheBosonicString715.3.1Mass-ShellCondition(OpenBosonicString)745.3.2MassSpectrum(OpenBosonicString)755.3.3AnalysisoftheMassSpectrum775.4Exercis

7、es796.IntroductiontoConformalFieldTheory806.1ConformalGroupindDimensions806.2ConformalAlgebrain2Dimensions836.3(Global)ConformalGroupin2Dimensions856.4ConformalFieldTheoriesindDimensions866.4.1ConstraintsofConfor