数学家用的量子场论

定　价：¥105.00

作　者：	英R.Ticciati著
出版社：	世界图书出版公司北京公司
丛编项：
标　签：	暂缺

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ISBN：	9787506250955	出版时间：	2001-06-01	包装：	胶版纸
开本：	22cm	页数：	699	字数：

内容简介

　　After completing my dissertation in differential geometry， I returned to Maharishi University of Management to join the faculty there. The greatest need for my services was in the physics department， and the chairman， the well-known John Hagelin， pointed the finger of authority and said 'quantum field theory！' The class to start in a few weeks. I laughed， but John was serious. Fortunately， I had audited Sidney Coleman's outstanding Harvard lectures and had taken very good notes. Equally fortunate， I had Robert Brandenburger's official aolutions to all the homework sets. I rolled up my sleeves and waded in. As we battled through the material， the beautiful architecture of Coleman's coures became apparent. It introduced the primary concepts - canonical quantization， renormalization， spin， functional integral quantization - one at a time and made each one practical before advancing to the next abstraction. It started with simple models and provided motivation for each elaboration. The students， however， pinned me to the board with questions about every step in the logic. Could I produce some mathematics to fill the gap？ Was there a physical principle which would justify the proposed step？ The standard references failed to meet the need， and for the most part I was stumped. It was a couple of years later， when the next group of graduate students was ripening， that I found time to think out some answers. The result was a draft of the first nine chapters of this book.此书为英文版！

作者简介

暂缺《数学家用的量子场论》作者简介

图书目录

Preface
Introduction
1.RelativisticQuantumMechanics
1.0Introduction
1.1One-ParticleStateSpace-Mathematics
1.2One-ParticleStateSpace-Physics
1.3TheActionofTranslationsonStates
1.4TheActionoftheLorentzGrouponStates
1.5RepresentingthePoincareGroup
1.6ThePositionOperator
1.7Summary
2.FockSpace,theScalarField,andCanonicalQuantization
2.0Introduction
2.1BosonicFockSpace
2.2HarmonicOscillatorReview
2.3ApplicationtoFockSpace
2.4TheFreeScalarField
2.5CanonicalQuantizationofClassicalMechanics
2.6CanonicalQuantizationofClassicalFields
2.7TheStructureoftheVacuumState
2.8Summary
3.SymmetriesandConservationLaws
3.0Introduction
3.1FourLevelsofSymmetryinallExample
3.2SymmetryandConservedQuantitiesinClassicalMechanics
3.3SymmetryandConservedQuantitiesinQuantumMechanics
3.4SymmetryandConservationLawsinClassicalFieldTheory
3.5Application:ComplexQuantumFields
3.6GroupsofMatricesandtheirLieAlgebras
3.7InternalSymmetriesinQuantumFieldTheory
3.8TheActionsandAlgebraofConservedQuantities
3.9TranslationSymmetry
3.10.LorentzSymmetry
3.11Application:QuantumNumbers
3.12ChargeConjugation
3.13Parity
3.14TimeReversal
3.15Summary
4.FromDyson'sFormulatoFeynmanRules
4.0Introduction
4.1TheInteractionPictureandDyson'sFormula
4.2TheWickExpansionoftheScatteringMatrix
4.3WickDiagrams
4.4TheCombinatoricsofWickDiagrams
4.5ReductiontoConnectedWickDiagrams
4.6FirstExample:ATime-DependentClassicalSource
4.7SecondExample:ATime-IndependentClassicalSource
4.8ComparisonwithClassicalFieldTheory
4.9FeynmanDiagramsandFeynmanRules
4.10ThirdExample:Tree-LevelScattering
4.11LorentzInvarianceandEliminationofVariables
4.12CrossingandMandelstamParameters
4.13PreliminaryPointsonRenormalization
4.14Summary
5.DifferentialTransitionProbabilitiesandPredictions
5.0Introduction
5.1DifferentialTransitionProbabilities
5.2TheInvariantDensityforTwo-ParticleFinalStates
5.3TheInvariantDensityforThree-ParticleFinalStates
5.4Decays
5.5CrossSections
5.6TheOpticalTheorem
5.7Summary
6.RepresentationsoftheLorentzGroup
6.0Introduction
6.1FromLieGrouptoLieAlgebraRepresentations
6.2DefinitionsforRepresentationTheory
6.3DetailedStructureofsu(2)andso(1,3)
6.4su(2)inParticular
6.5TheTensorProduct
6.6WeightsandTensorProducts
6.7TheRepresentationsofso(1,3)
6.8TensorProductsofso(1,3)Representations
6.9ComplexConjugation,Parity,andRestrictiontoRotations
6.10Vectors,Tensors,andSymmetry
6.11Summary
7.Two-ComponentSpinorFields
7.0Introduction
7.1TheLorentzGroupActiononSpinors
7.2TheLorentzGroupandSL(2,C)
7.3InvariantTermsfromSpinorsandVectors
7.4FermionicCalculus
7.5ClassicalMasslessWeylSpinors
7.6FreeMasslessWeylQuantumFields
7.7ConservedCurrentandQuantity
7.8Helicity
7.9AngularMomentumofaFreeSpinor
7.10ContractionsforMasslessWeylSpinors
7.11DefininganExample
7.12-FirstApplication
7.13-SecondApplication
7.14-ThirdApplication
7.15-ConclusionofExample
7.16Two-ComponentSpinorNotation
7.17MassiveWeylSpinors
7.18-EquationsofMotion,andDiracAlgebra
7.19Summary
8.Four-ComponentSpinorFields
8.0Introduction
8.1RepresentationsoftheDiracAlgebra
8.2BasicFeaturesofDiracAlgebra
8.3PolarizationSpinorsintheStandardRepresentation
8.4CanonicalQuantizationofDiracSpinors
8.5FeynmanRulesforDiracSpinors
8.6DiracAlgebra
8.7FierzTransformations
8.8DiracSpinorScatteringExample
8.9ChargeConjugation
8.10Parity
8.11TimeReversal
8.12TheActionofDiscreteSymmetriesonBilinearTerms
8.13CombinationsofC,P,andT
8.14Summary
9.VectorFieldsandGaugeInvariance
9.0Introduction
9.1TheLagrangianDensityandPlaneWaveSolutions
9.2QuantizationoftheMassiveVectorField
9.3FeynmanRulesfortheMassiveVectorField
9.4TheMasslessLimitoftheMassiveTheory
9.5ComptonScattering
9.6TheGaugePrinciple
9.7GaugeInvarianceandMinimalCoupling
9.8MassTermandCurrentConservation
9.9DiscreteSymmetries
9.10Summary
10.ReformulatingScatteringTheory
10.0Introduction
10.1GeneratingFunctionalsandGreenFunctions
10.2TheGeneratingFunctionalinPerturbationTheory
10.3GreenFunctionsandFeynmanDiagrams
10.4InandOutStates
10.5TheLSZReductionFormulaforScatteringAmplitudes
10.6ChangeinNotation
10.7ComputationwithBareFieldsandParameters
10.8ComputingwithRenormalizedFieldsandParameters
10.91PIGreenFunctionsandCountertermRenormalization
10.10Example:FieldandMassRenormalizationConditions
10.11Example:CouplingRenormalizationCondition
10.12ExtendingtheFormalismtoDiracFields
10.13DiracRenormalizationConditions
10.14ExtendingtheFormalismtoVectorFields
10.15Lehmann-KallenSpectralRepresentation
10.16ExtendingtheFormalismtoUnstableParticles
10.17ModelingUnstableParticles
10.18PropagationofUnstableParticles
10.19Summary
11.FunctionalIntegralQuantization
11.0Introduction
11.1DerivingtheFunctionalIntegralfromQuantumMechanics
11.2AnExample:theFreeParticle
11.3DetailsofFunctionalIntegration:OperatorOrdering
11.4-WickRotationofTime
11.5-EvaluatingGaussians
11.6FourierTransformofInnerProductsandOperators
11.7FunctionalIntegralQuantization:LagrangianForm
11.8-PerturbationExpansion
11.9-HamiltonianForm
11.10ExtensiontotheFreeMassiveVectorField
11.11FermionicFunctionalDifferentiation
11.12FunctionalDerivativeQuantizationforFermions
11.13Summary
12.QuantlzationofGaugeTheories
12.0Introduction
12.1MassiveSpinorQED
12.2MassiveScalarQED
12.3OutlineofFacldeev-PopovQuantizationofGaugeTheories
12.4QEDinCovariantGauge
12.5TheGeometryofGaugeFieldTheories
12.6ClassicalMinimally-CoupledGaugeTheories
12.7QuantizationofNon-AbelianGaugeTheories
12.8GlobalandLocalSpontaneousSymmetryBreaking
12.9Goldstone'sTheoremandtheHiggsMechanism
12.10QuantizationafterSpontaneousSymmetryBreaking
12.11Faddeev-PopovQuantizationRevisited
12.12Summary
13.AnomaliesandVacuainGaugeTheories
13.0Introduction
13.1PreservationofConservationLawsinBosonicTheories
13.2BreakdownofConservationLawsinFermionicTheories
13.3WickRotationandFermionicFunctionalCalculus
13.4TheAbelianAnomaly
13.5FunctionalJacobians
13.6LocalAnomalyTheorems
13.7BasicTopologyfortheDiscussionofGlobalAnomalies
13.8TheTopologyoftheGaugeGroup
13.9TheTopologyoftheSpaceofGaugePotentials
13.10TheGlobalAnomalyforQuantumGaugeTheories
13.11Summary
14.SU(3)RepresentationTheory
14.0Introduction
14.1SU(3)RepresentationsofSmallDegree
14.2InterpretationofSU(3)asFlavor
14.3InterpretationofSU(3)asColor
14.4SU(3)WeightDiagrams
14.5TensorRepresentations
14.6SplittingTensorProducts
14.7YoungDiagrams
14.8Summary
15.TheStructureoftheStandardModel
15.0Introduction
15.1TheElectroweakLagrangian
15.2-SyanetryBreaking
15.3-IdentifyingthePhoton
15.4-CovariantDerivative
15.5-ParticleMasses
15.6-TheCouplingsoftheVectorBosonstoLeptons
15.7-EffectiveFour-FermiInteractions
15.8-ThreeFamiliesofLeptons
15.9TheQCDLagrangian
15.10-DiagonalizingtheQuarkMassMatrices
15.11TheStandardModel:Consistency
15.12-LeptonandBaryonNumberViolation
15.13-GlobalAnomalies
15.14StrongInteractions:ApproximateSymmetries
15.15-TheStrongCPProblem
15.16Summary
16.Hadrons,FlavorSymmetry,andNucleon-PionInteractions
16.0Introduction
16.1Hadrons
16.2FlavorSymmetry:ActiononOctets
16.3-BaryonOctetMagneticMoments
16.4ConstituentQuarksandHadronMagneticMoments
16.5FlavorSymmetry-Gell-Mann-OkuboMassFormula
16.6-IsosingletMixing
16.7-ElectromagneticMassSplitting
16.8-LeptonicDecays
16.9Nucleon-PionTheory
16.10Nucleon-PionScattering
16.11TheModel
16.12-AbelianAnomaly
16.13Sommary
17.Tree-LevelApplicationsoftheStandardModel
17.0Introduction
17.1LeptonicInteractions
17.2Lepto-quarkOperators
17.3-ThePartonModel
17.4-ThePattonModelandModeCounting
17.5-QuarkAnnihilation
17.6-QuarkDecay
17.7Baryons:FormFactorsforCurrentMatrixElements
17.8-BDecays
17.9-FlavorSymmetryinOctetBDecays
17.10-TheGoldberger-TreimanRelation
17.11Summary
18.gegularizationandRenormalization
18.0Introduction
18.1FeynmanIntegralTechniqueforLoopDiagrams
18.2FeynmanIntegralsinEuclideanSpace
18.3TheGeneralCharacterofRegularization
18.4TheGeneralCharacterofRenormalization
18.5Regularization
18.6DimensionalRegularizationDefined
18.7DimensionalRegularizationApplied
18.8TheFFunction
18.9DiracAlgebrainDDimensions
18.10RegularizationofCompositeOperators
18.11RenormalizationofCompositeOperators
18.12TheAbelianAnomalyRevisited
18.13Summary
19.RenormalizationofQED:ThreePrimitiveDivergences
19.0Introduction
19.1TheCountertermLagrangianDensity
19.2RenormalizationConditions
19.3ChargeRenormalization
19.4ThePhotonSelf-EnergyFunction
19.5GaugeandPhotonPropagatorRenormalizationConditions
19.6ElectronSerf-EnergyFunction
19.7ElectronPropagatorRenormalizationConditions
19.8TheVertexCorrection
19.9TheInfraredDivergence
19.10LambShiftandAnomalousMagneticMoments
19.11RenormalizationbyMinimalSubtraction
19.12Summary
20.RenormalizationandPreservationofSymmetries
20.0Introduction
20.1SuperficialDegreeofDivergence
20.2TheForestFormula
20.3RenormalizationandGlobalSymmetry
20.4TheWard-TakahashiIdentity
20.5EffectiveClassicalAction
20.6PerturbativeWard-TakahashiIdentities
20.7-GaugeInvarianceofQED
20.8Slavnov-TaylorIdentity
20.9-RenormalizationandGaugeInvariance
20.10Summary
21.TheRenormalizationGroupEquations
21.0Introduction
21.1TheRenormalizationGroup
21.2ScaleInvariance,ScaleCovariance,andRGEs
21.3TheConstancyoftheBareLagrangian
21.4MinimalSubtractionandtheRenormalizationGroup
21.5RGEExample-ScalarTheory
21.6-SolvingtheRGEs
21.7-TheLeading-LogarithmApproximation
21.8FurtherExamples-QED
21.9-RGEsinYang-MillsTheories
21.10-QualitativeFeaturesofRGEs
21.11-RGEsforGreenFunctions
21.12ThePathtoUnifiedFieldTheories
21.13RenormalizabilityReconsidered
21.14Summary
Appendix
A.1ConstantsofParticlePhysics
A.2DiracAlgebra
A.3MiscellaneousConventionsandDefinitions
A.4FreeFields
A.5FunctionalIntegralQuantization
A.6Lagrangians
A.7TheStandardModelLagrangian
A.8FeynmanRules
A.9FeynmanIntegralTechniqueforLoopDiagrams
A.10DimensionalRegularization
A.11Amplitudes,DecayWidths,andCrossSections
References
Index