量子场论 第2卷 英文PDF电子书下载

15 NON-ABELIAN GAUGE THEORIES 1

15.1 Gauge Invariance 2

15.2 Gauge Theory Lagrangians and Simple Lie Groups 7

15.3 Field Equations and Conservation Laws 12

15.4 Quantization 14

15.5 The De Witt-Faddeev-Popov Method 19

15.6 Ghosts 24

15.7 BRST Symmetry 27

15.8 Generalizations of BRST Symmetry 36

15.9 The Batalin-Vilkovisky Formalism 42

Appendix A A Theorem Regarding Lie Algebras 50

Appendix B The Cartan Catalog 54

Problems 58

References 59

16 EXTERNAL FIELD METHODS 63

16.1 The Quantum Effective Action 63

16.2 Calculation of the Effective Potential 68

16.3 Energy Interpretation 72

16.4 Symmetries of the Effective Action 75

Problems 78

References 78

17 RENORMALIZATION OF GAUGE THEORIES 80

17.1 The Zinn-Justin Equation 80

17.2 Renormalization:Direct Analysis 82

17.3 Renormalization:General Gauge Theories 91

17.4 Background Field Gauge 95

17.5 A One-Loop Calculation in Background Field Gauge 100

Problems 109

References 110

18 RENORMALIZATION GROUP METHODS 111

18.1 Where do the Large Logarithms Come From? 112

18.2 The Sliding Scale 119

18.3 Varieties of Asymptotic Behavior 130

18.4 Multiple Couplings and Mass Effects 139

18.5 Critical Phenomena 145

18.6 Minimal Subtraction 148

18.7 Quantum Chromodynamics 152

18.8 Improved Perturbation Theory 157

Problems 158

References 159

19 SPONTANEOUSLY BROKEN GLOBAL SYMMETRIES 163

19.1 Degenerate Vacua 163

19.2 Coldstone Bosons 167

19.3 Spontaneously Broken Approximate Symmetries 177

19.4 Pions as Goldstone Bosons 182

19.5 Effective Field Theories:Pions and Nucleons 192

19.6 Effective Field Theories:General Broken Symmetries 211

19.7 Effective Field Theories:SU(3)×SU(3) 225

19.8 Anomalous Terms in Effective Field Theories 234

19.9 Unbroken Symmetries 238

19.10 The U(1) Problem 243

Problems 246

References 247

20 OPERATOR PRODUCT EXPANSIONS 252

20.1 The Expansion:Description and Derivation 253

20.2 Momentum Flow 255

20.3 Renormalization Group Equations for Coefficient Functions 263

20.4 Symmetry Properties of Coefficient Functions 265

20.5 Spectral Function Sum Rules 266

20.6 Deep Inelastic Scattering 272

20.7 Renormalons 283

Appendix Momentum Flow:The General Case 288

Problems 292

References 293

21 SPONTANEOUSLY BROKEN GAUGE SYMMETRIES 295

21.1 Unitarity Gauge 295

21.2 Renormalizable ξ-Gauges 300

21.3 The Electroweak Theory 305

21.4 Dynamically Broken Local Symmetries 318

21.5 Electroweak-Strong Unification 327

21.6 Superconductivity 332

Appendix General Unitarity Gauge 352

Problems 353

References 354

22 ANOMALIES 359

22.1 Theπ° Decay Problem 359

22.2 Transformation of the Measure:The Abelian Anomaly 362

22.3 Direct Calculation of Anomalies:The General Case 370

22.4 Anomaly-Free Gauge Theories 383

22.5 Massless Bound States 389

22.6 Consistency Conditions 396

22.7 Anomalies and Goldstone Bosons 408

Problems 416

References 417

23 EXTENDED FIELD CONFIGURATIONS 421

23.1 The Uses of Topology 422

23.2 Homotopy Groups 430

23.3 Monopoles 436

23.4 The Cartan-Maurer Integral Invariant 445

23.5 Instantons 450

23.6 The Theta Angle 455

23.7 Quantum Fluctuations around Extended Field Configurations 462

23.8 Vacuum Decay 464

Appendix A Euclidean Path Integrals 468

Appendix B A List of Homotopy Groups 472

Problems 473

References 474

AUTHOR INDEX 478

SUBJECT INDEX 484