Quantum Field Theory

Quantum Field Theory......Page 1
Half-Title......Page 2
Title-Page......Page 4
Copyright......Page 5
Dedication......Page 6
Contents......Page 8
Preface......Page 12
1.1 Quantum field theory......Page 14
1.2 Gravitation......Page 15
1.3 Strong interactions......Page 16
1.4 Weak interactions......Page 17
1.5 Leptonic quantum numbers......Page 19
1.6 Hadronic quantum numbers......Page 20
1.7 Resonances......Page 21
1.8 The quark model......Page 23
1.9 SU(2), SU(3), SU(4),.........Page 25
1.10 Dynamical evidence for quarks......Page 29
1.11 Colour......Page 32
1.12 QCD......Page 35
1.13 Weak interactions......Page 37
Guide to further reading......Page 38
2.1 Relativistic notation......Page 40
2.2 Klein-Gordon equation......Page 42
2.3 Dirac equation......Page 44
2.4 Prediction of antiparticles......Page 58
2.5 Construction of Dirac spinors: algebra of gamma matrices......Page 61
2.6 Non-relativistic limit and the electron magnetic moment......Page 68
2.7 The relevance of the Poincare group: spin operators and the zero mass limit......Page 70
2.8 Maxwell and Proca equation......Page 79
2.9 Maxwell’s equations and differential geometry......Page 84
Guide to further reading......Page 92
3 Lagrangian formulation, symmetries and gauge fields......Page 94
3.1 Lagrangian formulation of particle mechanics......Page 95
3.2 The real scalar field; variational principle and Noether’s theorem......Page 97
3.3 Complex scalar fields and the electromagnetic field......Page 106
3.4 Topology and the vacuum: the Bohm-Aharonov effect......Page 114
3.5 The Yang-Mills field......Page 121
3.6 The geometry of gauge fields......Page 128
Summary......Page 139
Guide to further reading......Page 140
4.1 The real Klein-Gordon field......Page 142
4.2 The complex Klein-Gordon field......Page 151
4.3 The Dirac field......Page 152
4.4 Electromagnetic field......Page 156
4.5 The massive vector field......Page 166
Guide to further reading......Page 168
5 Path integrals and quantum mechanics......Page 170
5.1 Path integral formulation of quantum mechanics......Page 171
5.2 Perturbation theory and the S matrix......Page 177
5.3 Coulomb scattering......Page 187
5.4 Functional calculus: differentiation......Page 189
5.5 Further properties of path integrals......Page 191
Appendix: some useful integrals......Page 196
Guide to further reading......Page 198
6.1 Generating functional for scalar fields......Page 200
6.2 Functional integration......Page 204
6.3 Free particie Green’s functions......Page 207
6.4 Generating functionals for interacting fields......Page 215
6.5 phi-4 theory......Page 218
6.6 Generating functional for connected diagrams......Page 225
6.7 Fermions and functional methods......Page 228
6.8 The S matrix and reduction formula......Page 234
6.9 Pion-nucleon scattering amplitude......Page 241
6.10 Scattering cross section......Page 249
Guide to further reading......Page 256
7.1 Propagators and gauge conditions in QED......Page 258
7.2 Non-Abelian gauge fields and the Faddeev-Popov method......Page 263
7.3 Self-energy operator and vertex function......Page 274
7.4 Ward-Takahashi identities in QED......Page 283
7.5 Becchi-Rouet-Stora transformation......Page 290
7.6 Slavnov-Taylor identities......Page 292
7.7 A note on ghosts and unitarity......Page 296
Guide to further reading......Page 301
8.1 What is the vacuum?......Page 303
8.2 The Goldstone theorem......Page 309
8.3 Spontaneous breaking of gauge symmetries......Page 314
8.4 Superconductivity......Page 318
8.5 The Weinberg-Salam model......Page 320
Guide to further reading......Page 328
9.1 Divergences in phi-4 theory......Page 331
9.2 Dimensional regularisation of phi-4 theory......Page 336
9.3 Renormalisation of phi-4 theory......Page 341
9.4 Renormalisation group......Page 347
9.5 Divergences and dimensional regularisation of QED......Page 352
9.6 1-loop renormalisation of QED......Page 361
9.7 Renormalisability of QED......Page 370
9.8 Asymptotic freedom of Yang-Mills theories......Page 377
9.9 Renormalisation of pure Yang Mills theorie......Page 385
9.11 Renormalisation of Yang-Mills theories with spontaneous symmetry breakdown......Page 398
Appendix A: integration in d dimensions......Page 405
Appendix B: the gamma function......Page 408
Summary......Page 410
Guide to further reading......Page 411
10 Topological objects in field theory......Page 414
10.1 The sine-Gordon kink......Page 415
10.2 Vortex lines......Page 419
10.3 The Dirac monopole......Page 426
10.4 The ’t Hooft-Polyakov monopole......Page 430
10.5 Instantons......Page 438
Guide to further reading......Page 448
Index......Page 451