Modern quantum field theory : a concise introduction / Tom Banks.

Format:

Book

Author/Creator:

Banks, Thomas.

Contributor:

Class of 1953 Fund.

Language:

English

Subjects (All):

Quantum field theory.

Physical Description:

271 pages ; 26 cm

Place of Publication:

Cambridge, UK ; New York : Cambridge University Press, 2008.

Summary:

Quantum field theory is a key subject in physics, with applications in particle and condensed matter physics. Treating a variety of topics that are only briefly touched on in other texts, this book provides a thorough introduction to the techniques of field theory.

The book covers Feynman diagrams and path integrals, and emphasizes the path integral approach, the Wilsonian approach to renormalization, and the physics of non-abelian gauge theory. It provides a thorough treatment of quark confinement and chiral symmetry breaking, topics not usually covered in other texts at this level. The Standard Model of particle physics is discussed in detail. Connections with condensed matter physics are explored, and there is a brief, but detailed, treatment of non-perturbative semi-classical methods (instantons and solitons).

Ideal for graduate students in high energy physics and condensed matter physics, the book contains many problems, providing students with hands-on experience with the methods of quantum field theory.

Contents:

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'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-1/2 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 [phi superscript 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

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.

Notes:

Includes bibliographical references and (pages [262]-267) and indexes.

Local Notes:

Acquired for the Penn Libraries with assistance from the Class of 1953 Fund.

ISBN:

9780521850827

0521850827

OCLC:

232605696

Online:

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