The quantum theory of fields, vol. 1 Foundations

1. HISTORICAL INTRODUCTION......Page 25
1.1 Relativistic Wave Mechanics......Page 27
1.2 The Birth of Quantum Field Theory......Page 39
1.3 The Problem of Infinities......Page 55
Bibliography......Page 63
References......Page 64
2.1 Quantum Mechanics......Page 73
2.2 Symmetries......Page 74
2.3 Quantum Lorentz Transformations......Page 79
2.5 One-Particle States......Page 86
2.6 Space Inversion and Time-Reversal......Page 98
2.7 Projective Representations*......Page 105
Appendix A. The Symmetry Representation Theorem......Page 115
Appendix В. Group Operators and Homotopy Classes......Page 120
Appendix С Inversions and Degenerate Multiplets......Page 124
Problems......Page 128
References......Page 129
3.1 'In' and 'Out' States......Page 131
3.2 The S-matrix ......Page 137
3.3 Symmetries of the S-Matrix......Page 140
3.4 Rates and Cross-Sections......Page 158
3.5 Perturbation Theory......Page 165
3.6 Implications of Unitarity......Page 171
3.7 Partial-Wave Expansions*......Page 175
3.8 Resonances*......Page 183
Problems......Page 189
References......Page 190
4. THE CLUSTER DECOMPOSITION PRINCIPLE......Page 193
4.1 Bosons and Fermions......Page 194
4.2 Creation and Annihilation Operators......Page 197
4.3 Cluster Decomposition and Connected Amplitudes......Page 201
4.4 Structure of the Interaction......Page 206
References......Page 213
5.1 Free Fields......Page 215
5.2 Causal Scalar Fields......Page 225
5.3 Causal Vector Fields......Page 231
5.4 The Dirac Formalism......Page 237
5.5 Causal Dirac Fields......Page 243
5.6 General Irreducible Representations of the Homogeneous Lorentz Group* ......Page 253
5.7 General Causal Fields* ......Page 257
5.8 The CPT Theorem......Page 268
5.9 Massless Particle Fields......Page 270
Problems......Page 279
References......Page 280
6.1 Derivation of the Rules......Page 283
6.2 Calculation of the Propagator......Page 298
6.3 Momentum Space Rules......Page 304
6.4 Off the Mass Shell......Page 310
Problems......Page 314
References......Page 315
7. THE CANONICAL FORMALISM......Page 316
7.1 Canonical Variables......Page 317
7.2 The Lagrangian Formalism......Page 322
73 Global Symmetries......Page 330
7.4 Lorentz Invariance......Page 338
7.5 Transition to Interaction Picture: Examples......Page 342
7.6 Constraints and Dirac Brackets......Page 349
7.7 Field Redefinitions and Redundant Couplings*......Page 355
Appendix. Dirac Brackets from Canonical Commutators......Page 356
Problems......Page 361
References......Page 362
8.1 Gauge Invariance......Page 363
8.2 Constraints and Gauge Conditions......Page 367
8.3 Quantization in Coulomb Gauge......Page 370
8.4 Electrodynamics in the Interaction Picture......Page 374
8.5 The Photon Propagator......Page 377
8.6 Feynman Rules for Spinor Electrodynamics......Page 379
8.7 Compton Scattering......Page 386
8.8 Generalization : p-form Gauge Fields*......Page 393
Appendix. Traces......Page 396
Problems......Page 398
References......Page 399
9. PATH-INTEGRAL METHODS......Page 400
9.1 The General Path-Integral Formula......Page 402
9.2 Transition to the S-Malrix......Page 409
9.3 Lagrangian Version of the Path-Integral Formula......Page 413
9.4 Path-Integral Derivation of Feynman Rules......Page 419
9.5 Path Integrals for Fermions......Page 423
9.6 Path-Integral Formulation of Quantum Electrodynamics......Page 437
9.7 Varieties of Statistics*......Page 442
Appendix. Gaussian Multiple Integrals......Page 444
References......Page 447
10.1 Symmetries......Page 449
10.2 Polology......Page 452
10.3 Field and Mass Renormalization......Page 460
10.4 Renormalized Charge and Ward Identities......Page 466
10.5 Gauge Invariance......Page 472
10.6 Electromagnetic Form Factors and Magnetic Moment......Page 476
10.7 The Källen-Lehmann Representation*......Page 481
10.8 Dispersion Relations*......Page 486
Problems......Page 493
References......Page 494
11.1 Counterterms......Page 496
11.2 Vacuum Polarization......Page 497
11.3 Anomalous Magnetic Moments and Charge Radii......Page 509
11.4 Electron Self-Energy......Page 517
Appendix. Assorted Integrals......Page 521
References......Page 522
12. GENERAL RENORMALIZATION THEORY......Page 523
12.1 Degrees of Divergence......Page 524
12.2 Cancellation of Divergences......Page 529
12.3 Is Renormalizability Necessary?......Page 540
12.4 The Floating Cutoff*......Page 549
Problems......Page 555
References......Page 556
13.1 Soft Photon Amplitudes......Page 558
13.2 Virtual Soft Photons......Page 563
13.3 Real Soft Photons; Cancellation of Divergences......Page 568
13.4 General Infrared Divergences......Page 572
13.5 Soft Photon Scattering*......Page 577
13.6 The External Field Approximation*......Page 580
References......Page 586
14. BOUND STATES IN EXTERNAL FIELDS......Page 588
14.1 The Dirac Equation......Page 589
14.2 Radiative Corrections in External Fields......Page 596
14.3 The Lamb Shift in Light Atoms......Page 602
Problems......Page 618
References......Page 620
AUTHOR INDEX......Page 621
SUBJECT INDEX......Page 626