现代量子场论简引

1 Introduction page 1

1.1 Preface and conventions 1

1.2 Why quantum field theory? 3

2 Quantum theory of free scalar fields 8

2.1 Local fields 10

2.2 Problems for Chapter 2 13

3 Interacting field theory 17

3.1 Schwinger.Dyson equations and functional integrals 17

3.2 Functional integral solution of the SD equations 20

3.3 Perturbation theory 24

3.4 Connected and 1-P(article) I(rreducible) Green functions 26

3.5 Legendre乫s trees 28

3.6 The Kallen.Lehmann spectral representation 30

3.7 The scattering matrix and the LSZ formula 32

3.8 Problems for Chapter 3 36

1 Introduction page 1

1.1 Preface and conventions 1

1.2 Why quantum field theory? 3

2 Quantum theory of free scalar fields 8

2.1 Local fields 10

2.2 Problems for Chapter 2 13

3 Interacting field theory 17

3.1 Schwinger.Dyson equations and functional integrals 17

3.2 Functional integral solution of the SD equations 20

3.3 Perturbation theory 24

3.4 Connected and 1-P(article) I(rreducible) Green functions 26

3.5 Legendre乫s trees 28

3.6 The Kallen.Lehmann spectral representation 30

3.7 The scattering matrix and the LSZ formula 32

3.8 Problems for Chapter 3 36

4 Particles of spin 1, and gauge invariance 38

4.1 Massive spinning particles 38

4.2 Massless particles with helicity 39

4.3 Field theory for massive spin-1 particles 40

4.4 Problems for Chapter 4 43

5 Spin-12

particles and Fermi statistics 44

5.1 Dirac, Majorana, and Weyl fields: discrete symmetries 49

5.2 The functional formalism for fermion fields 56

5.3 Feynman rules for Dirac fermions 58

5.4 Problems for Chapter 5 59

6 Massive quantum electrodynamics 62

6.1 Free the longitudinal gauge bosons! 64

6.2 Heavy-fermion production in electron.positron annihilation 65

6.3 Interaction with heavy fermions: particle paths and

external fields 68

6.4 The magnetic moment of a weakly coupled charged particle 69

6.5 Problems for Chapter 6 74

7 Symmetries, Ward identities, and Nambu.Goldstone bosons 76

7.1 Space-time symmetries 78

7.2 Spontaneously broken symmetries 81

7.3 Nambu.Goldstone bosons in the semi-classical expansion 84

7.4 Low-energy effective field theory of Nambu.Goldstone bosons 85

7.5 Problems for Chapter 7 89

8 Non-abelian gauge theory 93

8.1 The non-abelian Higgs phenomenon 96

8.2 BRST symmetry 97

8.3 A brief history of the physics of non-abelian gauge theory 99

8.4 The Higgs model, duality, and the phases of gauge theory 101

8.5 Confinement of monopoles in the Higgs phase 103

8.6 The electro-weak sector of the standard model 113

8.7 Symmetries and symmetry breaking in the strong interactions 116

8.8 Anomalies 118

8.9 Quantization of gauge theories in the Higgs phase 130

8.10 Problems for Chapter 8 132

9 Renormalization and effective field theory 137

9.1 Divergences in Feynman graphs 139

9.2 Cut-offs 142

9.3 Renormalization and critical phenomena 145

9.4 The renormalization (semi-)group in field theory 148

9.5 Mathematical (Lorentz-invariant, unitary) quantum field theory 154

9.6 Renormalization of 冇4 field theory 156

9.7 Renormalization-group equations in dimensional regularization 161

9.8 Renormalization of QED at one loop 164

9.9 Renormalization-group equations in QED 173

9.10 Why is QED IR-free? 178

9.11 Coupling renormalization in non-abelian gauge theory 181

9.12 Renormalization-group equations for masses and the hierarchy

problem 188

9.13 Renormalization-group equations for the S-matrix 191

9.14 Renormalization and symmetry 193

9.15 The standard model through the lens of renormalization 201

9.16 Problems for Chapter 9 203

10 Instantons and solitons 206

10.1 The most probable escape path 206

10.2 Instantons in quantum mechanics 207

10.3 Instantons and solitons in field theory 213

10.4 Instantons in the two-dimensional Higgs model 216

10.5 Monopole instantons in three-dimensional Higgs models 221

10.6 Yang.Mills instantons 226

10.7 Solitons 232

10.8 't Hooft.Polyakov monopoles 236

10.9 Problems for Chapter 10 239

11 Concluding remarks 242

Appendix A Books 245

Appendix B Cross sections 247

Appendix C Diracology 248

Appendix D Feynman rules 251

Appendix E Group theory and Lie algebras 256

Appendix F Everything else 260

References 262

Author index 268

Subject index 269

《现代量子场论简引（英文影印版）》是关于量子场论的专著，书中涵盖了很多其他同类书中没有或一笔带过的专题。本书侧重路径积分方法和威尔逊的重整化理论。对于夸克禁闭、手征对称性破缺的其他书中一般不做详细讨论的专题也做了详细介绍。本书还讨论了场论与凝聚态物质物理的联系以及非微扰半经典方法。
　　本书适合粒子物理、高能物理、凝聚态物质物理等领域的研究生和研究者阅读。

《现代量子场论简引（英文影印版）》是影印版学术专著，原书由剑桥大学出版社于2008年出版。作者是高能粒子物理和超弦理论方面极具影响的世界级专家，有着对物理学非常深刻的理解。量子场论是目前理论物理的基础理论，无论在粒子物理还是凝聚态物理中都占有极其重要的地位。本书最大的特点在于其"现代"性，关注了很多前沿课题，讲解非常有新意。无疑，对于理论物理领域的研究人员和学生来说，本书都是不可多得的佳作。