This volume describes the advances in the quantum theory of fields that have led to an understanding of the electroweak and strong interactions of the elementary particles. These interactions have all turned out to be governed by principles of gauge invariance, so we start here in Chapters 1'5-17 with gauge theories, generalizing the familiar gauge invariance of electrodynamics to non-Abelian Lie groups.

PREFACE

NOTATION

1 HISTORICAL INTRODUCTION

 1.1 Relativistic Wave Mechanics

 1.2 The Birth of Quantum Fiedld 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 Poincare Algebra

 2.5 One-Particle States

 2.6 Space Inversion and Time-Reversal

 2.7 Projective Representations

 AppendixA The Symmetry Representation Theorem

 AppendixB Group Operators and Homotopy Classes

 AppendixC 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 DECOMPOSITON 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

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 General Causal Fields

……

6 THE FEYNMAN RULES

7 THE CANONICAL FORMALISM

8 ELECTRODYNAMICS

9 PATH-INTEGRAL METHODS

10 NON-PERTURBATIVE METHODS

11 ONE-LOOP RADIATIVE CORRECTIONS IN QUANTUM ELECTRODYNAMICS

12 GENERAL RENORMALIZATION THEORY

13 INFRARED EFFECTS

14 BOUND STATES IN EXTERNAL FIELDS

AUTHOR INDEX

SUBJECT INDEX

OUTLINE OF VOLUMEⅡ