Gauge Theories of the Strong, Weak, and Electromagnetic Interactions

497 Pages·2013·5.51 MB·English

by  Chris Quigg

Gauge Theories of the Strong, Weak,
and Electromagnetic Interactions
SECOND EDITION
i

Gauge Theories of the Strong, Weak,
and Electromagnetic Interactions
SECOND EDITION
Chris Quigg
PRINCETON UNIVERSITY PRESS • PRINCETON AND OXFORD
iii
Firstedition,copyright(cid:1)c 1983,Addison-Wesley;1997,WestviewPress
Secondedition,copyright(cid:1)c 2013,PrincetonUniversityPress
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iv
«Où habitez-vous ? — Au voisinage de l’inconnu.»
«Que faites-vous ? — Je cherche à deviner la présence des secrets.»
— Jean-Bertrand Pontalis, En marge des jours
v

Contents
Preface xi
One
Introduction 1
1.1 ElementsoftheStandardModelofParticlePhysics 4
1.2 Leptons 6
1.3 Quarks 7
1.4 TheFundamentalInteractions 15
Problems 18
ForFurtherReading 21
References 23
Two
LagrangianFormalismandConservationLaws 25
2.1 Hamilton’sPrinciple 26
2.2 FreeFieldTheoryExamples 28
2.3 SymmetriesandConservationLaws 30
Problems 33
ForFurtherReading 35
References 37
Three
TheIdeaofGaugeInvariance 38
3.1 HistoricalPreliminaries 38
3.2 GaugeInvarianceinClassicalElectrodynamics 40
3.3 PhaseInvarianceinQuantumMechanics 42
3.4 SignificanceofPotentialsinQuantumTheory 44
3.5 PhaseInvarianceinFieldTheory 46
3.6 FeynmanRulesforElectromagnetism 50
Problems 52
ForFurtherReading 53
References 56
Four
Non-AbelianGaugeTheories 57
4.1 Motivation 57
4.2 Construction 58
4.3 SomePhysicalConsequences 63
4.4 Assessment 66
Problems 66
ForFurtherReading 69
References 70
viii • CONTENTS
Five
HiddenSymmetries 71
5.1 TheIdeaofSpontaneouslyBrokenSymmetries 72
5.2 SpontaneousBreakingofContinuousSymmetries 76
5.3 SpontaneousBreakingofaGaugeSymmetry 78
5.4 TheSigmaModel 81
5.5 SpontaneousBreakingofaNon-AbelianSymmetry 86
5.6 Prospects 87
Problems 88
ForFurtherReading 91
References 94
Six
ElectroweakInteractionsofLeptons 95
6.1 AnEffectiveLagrangianfortheWeakInteractions 96
6.2 IntermediateVectorBosons:AFirstLook 110
6.3 TheStandardElectroweakTheoryofLeptons 120
6.4 Neutral-CurrentInteractionsamongLeptons 135
6.5 TheHiggsBoson:AFirstLook 146
6.6 TheHiggsBoson,AsymptoticBehavior,
andthe1-TeVScale 151
6.7 NeutrinoMixingandNeutrinoMass 156
6.8 RenormalizabilityoftheTheory 166
6.9 InterimAssessment 170
Problems 171
ForFurtherReading 177
References 183
Seven
ElectroweakInteractionsofQuarks 187
7.1 TheStandardElectroweakTheory:Preliminaries 188
7.2 ElectroweakGaugeBosons 194
7.3 Electron–PositronAnnihilations 198
7.4 DeeplyInelasticLepton–HadronScattering 205
7.5 Hadron–HadronInteractions 223
7.6 FurtherTestsoftheElectroweakTheory 229
7.7 ABriefLookatQuantumCorrections 231
7.8 TheScaleofFermionMasses 236
7.9 SearchfortheHiggsBoson 237
7.10 IncompletenessoftheElectroweakTheory 241
7.11 TheHierarchyProblem 244
7.12 TheVacuumEnergyProblem 246
7.13 Reflections 247
Problems 249
ForFurtherReading 258
References 263
Eight
StrongInteractionsamongQuarks 269
8.1 AColorGaugeTheory 270
8.2 ChargeRenormalizationinElectrodynamics 281
CONTENTS • ix
8.3 TheRunningCouplingConstantinQCD 294
8.4 PerturbativeQCD:AFirstExample 303
8.5 QCDCorrectionstoDeeplyInelasticScattering 308
8.6 JetsinHadron–HadronCollisions 325
8.7 Two-PhotonProcessesandthePhoton-StructureFunction 328
8.8 ColorConfinement 336
8.9 QCD-inducedElectroweakSymmetryBreaking 341
8.10 The1/NExpansion 345
8.11 Strong-InteractionSymmetries 352
8.12 Assessment 356
Problems 358
ForFurtherReading 369
References 381
Nine
UnifiedTheories 387
9.1 WhyUnify? 389
9.2 TheSU(5)Model 391
9.3 Coupling-ConstantUnification 402
9.4 NucleonDecay 408
9.5 TheBaryonNumberoftheUniverse 410
9.6 TheProblemofFermionMasses 414
9.7 Assessment 416
Problems 418
ForFurtherReading 423
References 427
Epilogue 430
AppendixA NotationsandConventions 433
A.1 Four-VectorsandScalarProduct 433
A.2 DiracMatrices 434
A.3 TraceTheoremsandTensorContractions 436
A.4 DiracEquationandDiracSpinors 437
A.5 ColorAlgebra 440
A.6 Weyl–vanderWaerdenSpinors 444
References 445
AppendixB ObservablesandFeynmanRules 447
B.1 Phase-SpaceFormulas:DecayRatesandCrossSections 447
B.2 FeynmanRules:Generalities 448
B.3 FeynmanIntegrals 450
B.4 RegularizationProcedures 452
B.5 FeynmanRules:Electrodynamics 453
ForFurtherReading 454
References 456