1Introductionpage1
1.1Prefaceandconventions1
1.2Whyquantumfieldtheory?3
2Quantumtheoryoffreescalarfields8
2.1Localfields10
2.2ProblemsforChapter213
3Interactingfieldtheory17
3.1Schwinger.Dysonequationsandfunctionalintegrals17
3.2FunctionalintegralsolutionoftheSDequations20
3.3Perturbationtheory24
3.4Connectedand1-P(article)I(rreducible)Greenfunctions26
3.5Legendre乫strees28
3.6TheKallen.Lehmannspectralrepresentation30
3.7ThescatteringmatrixandtheLSZformula32
3.8ProblemsforChapter336
4Particlesofspin1,andgaugeinvariance38
4.1Massivespinningparticles38
4.2Masslessparticleswithhelicity39
4.3Fieldtheoryformassivespin-1particles40
4.4ProblemsforChapter443
5Spin-12
particlesandFermistatistics44
5.1Dirac,Majorana,andWeylfields:discretesymmetries49
5.2Thefunctionalformalismforfermionfields56
5.3FeynmanrulesforDiracfermions58
5.4ProblemsforChapter559
6Massivequantumelectrodynamics62
6.1Freethelongitudinalgaugebosons!64
6.2Heavy-fermionproductioninelectron.positronannihilation65
6.3Interactionwithheavyfermions:particlepathsand
externalfields68
6.4Themagneticmomentofaweaklycoupledchargedparticle69
6.5ProblemsforChapter674
7Symmetries,Wardidentities,andNambu.Goldstonebosons76
7.1Space-timesymmetries78
7.2Spontaneouslybrokensymmetries81
7.3Nambu.Goldstonebosonsinthesemi-classicalexpansion84
7.4Low-energyeffectivefieldtheoryofNambu.Goldstonebosons85
7.5ProblemsforChapter789
8Non-abeliangaugetheory93
8.1Thenon-abelianHiggsphenomenon96
8.2BRSTsymmetry97
8.3Abriefhistoryofthephysicsofnon-abeliangaugetheory99
8.4TheHiggsmodel,duality,andthephasesofgaugetheory101
8.5ConfinementofmonopolesintheHiggsphase103
8.6Theelectro-weaksectorofthestandardmodel113
8.7Symmetriesandsymmetrybreakinginthestronginteractions116
8.8Anomalies118
8.9QuantizationofgaugetheoriesintheHiggsphase130
8.10ProblemsforChapter8132
9Renormalizationandeffectivefieldtheory137
9.1DivergencesinFeynmangraphs139
9.2Cut-offs142
9.3Renormalizationandcriticalphenomena145
9.4Therenormalization(semi-)groupinfieldtheory148
9.5Mathematical(Lorentz-invariant,unitary)quantumfieldtheory154
9.6Renormalizationof冇4fieldtheory156
9.7Renormalization-groupequationsindimensionalregularization161
9.8RenormalizationofQEDatoneloop164
9.9Renormalization-groupequationsinQED173
9.10WhyisQEDIR-free?178
9.11Couplingrenormalizationinnon-abeliangaugetheory181
9.12Renormalization-groupequationsformassesandthehierarchy
problem188
9.13Renormalization-groupequationsfortheS-matrix191
9.14Renormalizationandsymmetry193
9.15Thestandardmodelthroughthelensofrenormalization201
9.16ProblemsforChapter9203
10Instantonsandsolitons206
10.1Themostprobableescapepath206
10.2Instantonsinquantummechanics207
10.3Instantonsandsolitonsinfieldtheory213
10.4Instantonsinthetwo-dimensionalHiggsmodel216
10.5Monopoleinstantonsinthree-dimensionalHiggsmodels221
10.6Yang.Millsinstantons226
10.7Solitons232
10.8'tHooft.Polyakovmonopoles236
10.9ProblemsforChapter10239
11Concludingremarks242
AppendixABooks245
AppendixBCrosssections247
AppendixCDiracology248
AppendixDFeynmanrules251
AppendixEGrouptheoryandLiealgebras256
AppendixFEverythingelse260
References262
Authorindex268
Subjectindex269
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