1 HISTORICAL INTRODUCTION 1
1.1 Relativistic Wave Mechanics 3
1.2 The Birth of Quantum Field Theory 15
1.3 The Problem of Infinities 31
Bibliography 39
References 40
2 RELATIVISTIC QUANTUM MECHANICS 49
2.1 Quantum Mechanics 49
2.2 Symmetries 50
2.3 Quantum Lorentz Transformations 55
2.4 The Poincaré Algebra 58
2.5 One-Particle States 62
2.6 Space Inversion and Time-Reversal 74
2.7 Projective Representations 81
Appendix A The Symmetry Representation Theorem 91
Appendix B Group Operators and Homotopy Classes 96
Appendix C Inversions and Degenerate Multiplets 100
Problems 104
References 105
3 SCATTERING THEORY 107
3.1 'In'and'Out'States 107
3.2 The S-matrix 113
3.3 Symmetries of the S-Matrix 116
3.4 Rates and Cross-Sections 134
3.5 Perturbation Theory 141
3.6 Implications of Unitarity 147
3.7 Partial-Wave Expansions 151
3.8 Resonances 159
Problems 165
References 166
4 THE CLUSTER DECOMPOSITION PRINCIPLE 169
4.1 Bosons and Fermions 170
4.2 Creation and Annihilation Operators 173
4.3 Cluster Decomposition and Connected Amplitudes 177
4.4 Structure of the Interaction 182
Problems 189
References 189
5 QUANTUM FIELDS AND ANTIPARTICLES 191
5.1 Free Fields 191
5.2 Causal Scalar Fields 201
5.3 Causal Vector Fields 207
5.4 The Dirac Formalism 213
5.5 Causal Dirac Fields 219
5.6 General Irreducible Representations of the Homogeneous Lorentz Group 229
5.7 Geueral Causal Fields 233
5.8 The CPT Theorem 244
5.9 Massless Particle Fields 246
Problems 255
References 256
6 THE FEYNMAN RULES 259
6.1 Derivation of the Rules 259
6.2 Calculation of the Propagator 274
6.3 Momentum Space Rules 280
6.4 Off the Mass Shell 286
Problems 290
References 291
7 THE CANONICAL FORMALISM 292
7.1 Canonical Variables 293
7.2 The Lagrangian Formalism 298
7.3 Global Symmetries 306
7.4 Lorentz Onvariance 314
7.5 Transition to Interaction Picture:Examples 318
7.6 Constraints and Dirac Brackets 325
7.7 Field Redefinitions and Redundant Couplings 331
Appendix Dirac Brackets from Canonical Commutators 332
Problems 337
References 338
8 ELECTRODYNAMICS 339
8.1 Gauge Invariance 339
8.2 Constraints and Gauge Conditions 343
8.3 Quantization in Coulomb Gauge 346
8.4 Electrodynamics in the Interaction Picture 350
8.5 The Photon Propagator 353
8.6 Feynman Rules for Spinor Electrodynamics 355
8.7 Compton Scattering 362
8.8 Generalization:p-form Gauge Fields 369
Appendix Traces 372
Problems 374
References 375
9 PATH-INTEGRAL METHODS 376
9.1 The General Path-Integral Formula 378
9.2 Transition to the S-Matrix 385
9.3 Lagrangian Version of the Path-Integral Formula 389
9.4 Path-Integral Derivation of Feynman Rules 395
9.5 Path Integrals for Fermions 399
9.6 Path-Integral Formulation of Quantum Electrodynamics 413
9.7 Varieties of Statistics 418
Appendix Gaussian Multiple Integrals 420
Problems 423
References 423
10 NON-PERTURBATIVE METHODS 425
10.1 Symmetries 425
10.2 Polology 428
10.3 Field and Mass Renormalization 436
10.4 Renormalized Charge and Ward Identities 442
10.5 Gauge Invariance 448
10.6 Electromagnetic Form Factors and Magnetic Moment 452
10.7 The K？llen-Lehmann Representation 457
10.8 Dispersion Relations 462
Problems 469
References 470
11 ONE-LOOP RADIATIVE CORRECTIONS IN QUANTUM ELECTRODYNAMICS 472
11.1 Counterterms 472
11.2 Vacuum Polarization 473
11.3 Anomalous Magnetic Moments and Charge Radii 485
11.4 Electron Self-Energy 493
Appendix Assorted Integrals 497
Problems 498
References 498
12 GENERAL RENORMALIZATION THEORY 499
12.1 Degrees of Divergence 500
12.2 Cancellation of Divergences 505
12.3 Is Renormalizability Necessary? 516
12.4 The Floating Cutoff 525
12.5 Accidental Symmetries 529
Problems 531
References 532
13 INFRARED EFFECTS 534
13.1 Soft Photon Amplitudes 534
13.2 Virtual Soft Photons 539
13.3 Real Soft Photons;Cancellation of Divergences 544
13.4 General Infrared Divergences 548
13.5 Soft Photon Scattering 553
13.6 The External Field Approximation 556
Problems 562
References 562
14 BOUND STATES IN EXTERNAL FIELDS 564
14.1 The Dirac Equation 565
14.2 Radiative Corrections in External Fields 572
14.3 The Lamb Shift in Light Atoms 578
Problems 594
References 595
AUTHOR INDEX 597
SUBJECT INDEX 602