量子场论简论

Preface

Convention,Notation,andUnits

PARTIMOTIVATIONANDFOUNDATION

I.1WhoNeedsIt?

I.2PathIntegralFormulationofQuantumPhysics

I.3FromMattresstoField

I.4FromFieldtoParticletoForce

I.5CoulombandNewton:RepulsionandAttraction

I.6InverseSquareLawandtheFloating3-Brane

I.7FeynmanDiagrams

I.8QuantizingCanonicallyandDisturbingtheVacuum

I.9Symmetry

I.10FieldTheoryinCurvedSpacetime

I.11FieldTheoryRedux

PARTIIDIRACANDTHESPINOR

II.1TheDiracEquation

II.2QuantizingtheDiracField

II.3LorentzGroupandWeylSpinors

II.4Spin-StatisticsConnection

II.5VacuumEnergy,GrassmannIntegrals,andFeynmanDiagramsforFermions

II.6ElectronScatteringandGaugeInvariance

II.7DiagrammaticProofofGaugeInvariance

PARTIIIRENORMALIZATIONANDGAUGEINVARIANCE

III.1CuttingOffOurIgnorance

III.2RenormalizableversusNonrenormalizable

III.3CountertermsandPhysicalPerturbationTheory

III.4GaugeInvariance:APhotonCanFindNoRest

III.5FieldTheorywithoutRelativity

III.6TheMagneticMomentoftheElectron

III.7PolarizingtheVacuumandRenormalizingtheCharge

PARTIVSYMMETRYANDSYMMETRYBREAKING

IV.1SymmetryBreaking

IV.2ThePionasaNambu-GoldstoneBoson

IV.3EffectivePotential

IV.4MagneticMonopole

IV.5NonabelianGaugeTheory

IV.6TheAnderson-HiggsMechanism

IV.7ChiralAnomaly

PARTVFIELDTHEORYANDCOLLECTIVEPHENOMENA

V.1Superfluids

V.2Euclid,Boltzmann,Hawking,andFieldTheoryatFiniteTemperature

V.3Landau-GinzburgTheoryofCriticalPhenomena

V.4Superconductivity

V.5PeierlsInstability

V.6Solitons

V.7Vortices,Monopoles,andInstantons

PARTVIFIELDTHEORYANDCONDENSEDMATTER

VI.1FractionalStatistics,Chern-SimonsTerm,andTopologicalFieldTheory

VI.2QuantumHallFluids

VI.3Duality

VI.4TheaModelsasEffectiveFieldTheories

VI.5FerromagnetsandAntiferromagnets

VI.6SurfaceGrowthandFieldTheory

VI.7Disorder:ReplicasandGrassmannianSymmetry

VI.8RenormalizationGroupFlowasaNaturalConceptinHighEnergyandCondensedMatterPhysics

PARTVIIGRANDUNIFICATION

VII.1QuantizingYang-MillsTheoryandLatticeGaugeTheory

VII.2ElectroweakUnification

VII.3QuantumChromodynamics

VII.4LargeNExpansion

VII.5GrandUnification

VII.6ProtonsAreNotForever

VII.7SO(10)Unification

PARTVIIIGRAVITYANDBEYOND

VIII.1GravityasaFieldTheoryandtheKaluza-KleinPicture

VIII.2TheCosmologicalConstantProblemandtheCosmicCoincidenceProblem

VIII.3EffectiveFieldTheoryApproachtoUnderstandingNatu.r

VIII.4Supersymmetry:AVeryBriefIntroduction

VIII.5AGlimpseofStringTheoryasa2-Dimensional

FieldTheoryClosingWords

APPENDIXES

AGaussianIntegrationandtheCentralIdentityofQuantumFieldTheory

BABriefReviewofGroupTheory

CFeynmanRules

DVariousIdentitiesandFeynmanIntegrals

EDottedandUndottedIndicesandtheMajoranaSpinor

SolutionstoSelectedExercises

FurtherReading

Index

　　Asastudent,Iwasrearingatthebit,afteracourseonquantummechanics,tolearnquantumfieldtheory,butthebooksonthesubjectallseemedsoformidable.Fortunately,IcameacrossalittlebookbyMandlonfieldtheory,whichgavemeatasteofthesubjectenablingmetogoonandtacklethemoresubstantivetexts.IhavesincelearnedthatotherphysicistsofmygenerationhadsimilargoodexperienceswithMandl.