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Contents Preface xiChapter 1 Notation and Conventions 1.1 PROBLEMS Chapter 2 Review of Perturbative Field Theory 2.1 CREATION AND ANNIHILATION OPERATORS 2.2 LAGRANGIAN FIELD THEORY 2.3 THE HERMITIAN SCALAR FIELD 2.3.1 The Lagrangian and Equations of Motion 2.3.2 The Free Hermitian Scalar Field 2.3.3 The Feynman Rules 2.3.4 Kinematics and the Mandelstam Variables 2.3.5 The Cross Section and Decay Rate Formulae 2.3.6 Loop Effects 2.4 THE COMPLEX SCALAR FIELD 2.4.1 U (1) Phase Symmetry and the Noether Theorem 2.5 ELECTROMAGNETIC AND VECTOR FIELDS 2.5.1 Massive Neutral Vector Field 2.6 ELECTROMAGNETIC INTERACTION OF CHARGED PIONS 2.7 THE DIRAC FIELD 2.7.1 The Free Dirac Field 2.7.2 Dirac Matrices and Spinors 2.8 QED FOR ELECTRONS AND POSITRONS 2.9 SPIN EFFECTS AND SPINOR CALCULATIONS 2.10 THE DISCRETE SYMMETRIES P , C, CP , T , AND CP T 2.11 TWO-COMPONENT NOTATION AND INDEPENDENT FIELDS 2.12 QUANTUM ELECTRODYNAMICS (QED) 2.12.1 Higher-Order Effects 2.12.2 The Running Coupling 2.12.3 Tests of QED 2.12.4 The Role of the Strong Interactions 2.13 OPERATOR DIMENSIONS AND CLASSIFICATION v vi Contents 2.14 MASS AND KINETIC MIXING 2.15 PROBLEMS Chapter 3 Lie Groups, Lie Algebras, and Symmetries 3.1 BASIC CONCEPTS 3.1.1 Groups and Representations 3.1.2 Examples of Lie Groups 3.1.3 More on Representations and Groups 3.2 GLOBAL SYMMETRIES IN FIELD THEORY 3.