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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