1 HISTORICAL INTRODUCTION

1.1 Relativistic Wave Mechanics

1.2 The Birth of Quantum Field Theory

1.3 The Problem of Infinities

Bibliography

References

2 RELATIVISTIC QUANTUM MECHANICS

2.1 Quantum Mechanics

2.2 Symmetries

2.3 Quantum Lorentz Transformations

2.4 The Poincaré Algebra

2.5 One-Particle States

2.6 Space Inversion and Time-Reversal

2.7 Projective Representations

Appendix A The Symmetry Representation Theorem

Appendix B Group Operators and Homotopy Classes

Appendix C Inversions and Degenerate Multiplets

Problems

References

3 SCATTERING THEORY

3.1 'In'and'Out'States

3.2 The S-matrix

3.3 Symmetries of the S-Matrix

3.4 Rates and Cross-Sections

3.5 Perturbation Theory

3.6 Implications of Unitarity

3.7 Partial-Wave Expansions

3.8 Resonances

Problems

References

4 THE CLUSTER DECOMPOSITION PRINCIPLE

4.1 Bosons and Fermions

4.2 Creation and Annihilation Operators

4.3 Cluster Decomposition and Connected Amplitudes

4.4 Structure of the Interaction

Problems

References

5 QUANTUM FIELDS AND ANTIPARTICLES

5.1 Free Fields

5.2 Causal Scalar Fields

5.3 Causal Vector Fields

5.4 The Dirac Formalism

5.5 Causal Dirac Fields

5.6 General Irreducible Representations of the Homogeneous Lorentz Group

5.7 Geueral Causal Fields

5.8 The CPT Theorem

5.9 Massless Particle Fields

Problems

References

6 THE FEYNMAN RULES

6.1 Derivation of the Rules

6.2 Calculation of the Propagator

6.3 Momentum Space Rules

6.4 Off the Mass Shell

Problems

References

7 THE CANONICAL FORMALISM

7.1 Canonical Variables

7.2 The Lagrangian Formalism

7.3 Global Symmetries

7.4 Lorentz Onvariance

7.5 Transition to Interaction Picture:Examples

7.6 Constraints and Dirac Brackets

7.7 Field Redefinitions and Redundant Couplings

Appendix Dirac Brackets from Canonical Commutators

Problems

References

8 ELECTRODYNAMICS

8.1 Gauge Invariance

8.2 Constraints and Gauge Conditions

8.3 Quantization in Coulomb Gauge

8.4 Electrodynamics in the Interaction Picture

8.5 The Photon Propagator

8.6 Feynman Rules for Spinor Electrodynamics

8.7 Compton Scattering

8.8 Generalization:p-form Gauge Fields

Appendix Traces

Problems

References

9 PATH-INTEGRAL METHODS

9.1 The General Path-Integral Formula

9.2 Transition to the S-Matrix

9.3 Lagrangian Version of the Path-Integral Formula

9.4 Path-Integral Derivation of Feynman Rules

9.5 Path Integrals for Fermions

9.6 Path-Integral Formulation of Quantum Electrodynamics

9.7 Varieties of Statistics

Appendix Gaussian Multiple Integrals

Problems

References

10 NON-PERTURBATIVE METHODS

10.1 Symmetries

10.2 Polology

10.3 Field and Mass Renormalization

10.4 Renormalized Charge and Ward Identities

10.5 Gauge Invariance

10.6 Electromagnetic Form Factors and Magnetic Moment

10.7 The K？llen-Lehmann Representation

10.8 Dispersion Relations

Problems

References

11 ONE-LOOP RADIATIVE CORRECTIONS IN QUANTUM ELECTRODYNAMICS

11.1 Counterterms

11.2 Vacuum Polarization

11.3 Anomalous Magnetic Moments and Charge Radii

11.4 Electron Self-Energy

Appendix Assorted Integrals

Problems

References

12 GENERAL RENORMALIZATION THEORY

12.1 Degrees of Divergence

12.2 Cancellation of Divergences

12.3 Is Renormalizability Necessary?

12.4 The Floating Cutoff

12.5 Accidental Symmetries

Problems

References

13 INFRARED EFFECTS

13.1 Soft Photon Amplitudes

13.2 Virtual Soft Photons

13.3 Real Soft Photons;Cancellation of Divergences

13.4 General Infrared Divergences

13.5 Soft Photon Scattering

13.6 The External Field Approximation

Problems

References

14 BOUND STATES IN EXTERNAL FIELDS

14.1 The Dirac Equation

14.2 Radiative Corrections in External Fields

14.3 The Lamb Shift in Light Atoms

Problems

References

AUTHOR INDEX

SUBJECT INDEX