PrefaceGeneral References1. Classical Theory 1.1 Principle of Least Action1.1. 1 Classical Motion1.1. 2 Electromagnetic Field as an Infinite Dynamical System1.1. 3 Electromagnetic Interaction of a Point Particle 1.2 Symmetries and Conservation Laws1.2. 1 Fundamental Invariants1.2. 2 Energy Momentum Tensor1.2. 3 Internal Symmetries 1.3 Propagation and Radiation1.3. 1 Green Functions1.3. 2 Radiation2. The Dirac Equation 2.1 Toward a Relativistic Wave Equation2.1. 1 Quantum Mechanics and Relativity2.1. 2 The Dirac Equation2.1. 3 Relativistic Covariance 2.2 Physical Content2.2. 1 Plane Wave Solutions and Projectors2.2. 2 Wave Packets2.2. 3 Electromagnetic Coupling2.2. 4 Foldy-Wouthuysen Transformation 2.3 Hydrogen-like Atoms2.3. 1 Nonrelativistic versus Relativistic Spectrum2.3. 2 Dirac Theory 2.4 Hole Theory and Charge Conjugation2.4. 1 Reinterpretation of Negative Energy Solutions2.4. 2 Charge Conjugation2.4. 3 Zero-Mass Particles 2.5 Dirac Propagator2.5. 1 Free Propagator2.5. 2 Propagation in an Arbitrary External Electromagnetic Field2.5. 3 Application to the Coulomb Scattering2.5. 4 Fock-Schwinger Proper Time Method3. Quantization--Free Fields 3.1 Canonical Quantization3.1. 1 General Formulation3.1. 2 Scalar Field3.1. 3 Charged Scalar Field3.1. 4 Time-Ordered Product3.1. 5 Thermodynamic Equilibrium 3.2 Quantized Radiation Field3.2. 1 Indefinite Metric3.2. 2 Propagator3.2. 3 Massive Vector Field3.2. 4 Vacuum Fluctuations 3.3 Dirac Field and Exclusion Principle3.3. 1 Anticommutators3.3. 2 Fock Space for Fermions3.3. 3 Relation between Spin and Statistics--Propagator 3.4 Discrete Symmetries3.4. 1 Parity3.4. 2 Charge Conjugation3.4. 3 Time Reversal3.4. 4 Summary4. Interaction with an External Field 4.1 Quantized Electromagnetic Field Interacting with a Classical Source4.1. 1 Emission Probabilities4.1. 2 Emitted Energy and the Infrared Catastrophe4.1. 3 Induced Absorption and Emission4.1. 4 S Matrix and Evolution Operator 4.2 Wick's Theorem4.2. 1 Bose Fields4.2. 2 Fermi Fields4.2. 3 General Case 4.3 Quantized Dirac Field Interacting with a Classical Potential4.3. 1 General Formalism4.3. 2 Emission Rate to Lowest Order4.3. 3 Pair Creation in a Constant Uniform Electric Field4.3. 4 The Euler-Heisenberg Effective Lagrangian5. Elementary Processes 5.1 S Matrix and Asymptotic Theory5.1. 1 Cross Sections5.1. 2 Asymptotic Theory5.1. 3 Reduction Formulas5.1. 4 Generating Functional5.1. 5 Connected Parts5.1. 6 Fermions5.1. 7 Photons 5.2 Applications5.2. 1 Compton Effect5.2. 2 Pair Annihilation5.2. 3 Positronium Lifetime5.2. 4 Bremsstrahlung 5.3 Unitarity and Causality5.3. 1 Unitarity and Partial Wave Decomposition5.3. 2 Causality and Analyticity5.3. 3 The Jost-Lehmann-Dyson Representation5.3. 4 Forward Dispersion Relations5.3. 5 Momentum Transfer Analyticity6. Perturbation Theory 6.1 Interaction Representation and Feynman Rules6.1. 1 Self-Interacting Scalar Field6.1. 2 Feynman Rules for Spinor Electrodynamics6.1. 3 Electron-Electron and Electron-Positron Scattering6.1. 4 Scalar Electrodynamics 6.2 Diagrammatics6.2. 1 Loopwise Expansion6.2. 2 Truncated and Proper Diagrams6.2. 3 Parametric Representation6.2. 4 Euclidean Green Functions 6.3 Analyticity Properties6.3. 1 Landau Equations6.3. 2 Real Singularities6.3. 3 Real Singularities of Simple Diagrams6.3. 4 Physical-Region Singularities. Cutkosky Rules7. Radiative Corrections 7.1 One-Loop Renormalization7.1. 1 Vacuum Polarization7.1. 2 Electron Propagator7.1. 3 Vertex Function7.1. 4 Summary 7.2 Radiative Corrections to the Interaction with an External Field7.2. 1 Effective Interaction and Anomalous Magnetic Moment7.2. 2 Radiative Corrections to Coulomb Scattering7.2. 3 Soft Bremsstrahlung7.2. 4 Finite Inclusive Cross Section 7.3 New Effects7.3. 1 Photon-Photon Scattering7.3. 2 Lamb Shift7.3. 3 Van der Waals Forces at Large Distances8. Renormalization 8.1 Regularization and Power Counting8.1. 1 Introduction8.1. 2 Regularization8.1. 3 Power Counting8.1. 4 Convergence Theorem 8.2 Renormalization8.2. 1 Normalization Conditions and Structure of the Counterterms8.2. 2 Bogoliubov's Recursion Formula8.2. 3 Zimmermann's Explicit Solution8.2. 4 Renormalization in Parametric Space8.2. 5 Finite Renormalizations8.2. 6 Composite Operators 8.3 Zero-Mass Limit, Asymptotic Behavior, and Weinberg's Theorem8.3. 1 Massless Theories8.3. 2 Ultraviolet Behavior and Weinberg's Theorem 8.4 The Case of Quantum Electrodynamics8.4. 1 Formal Derivation of the Ward-Takahashi Identities8.4. 2 Pauli-Villars Regularization to All Orders8.4. 3 Renormalization8.4. 4 Two-Loop Vacuum Polarization9. Functional Methods 9.1 Path Integrals9.1. 1 The Role of the Classical Action in Quantum Mechanics9.1. 2 Trajectories in the Bargmann-Fock Space9.1. 3 Fermion Systems 9.2 Relativistic Formulation9.2. 1 S Matrix and Green Functions in Terms of Path Integrals9.2. 2 Effective Action and Steepest-Descent Method 9.3 Constrained Systems9.3. 1 General Discussion9.3. 2 The Electromagnetic Field as an Example 9.4 Large Orders in Perturbation Theory9.4. 1 Introduction9.4. 2 Anharmonic Oscillator10. Integral Equations and Bound-State Problems 10.1 The Dyson-Schwinger Equations10.1. 1 Field Equations10.1. 2 Renormalization 10.2 Relativistic Bound States10.2. 1 Homogeneous Bethe-Salpeter Equation10.2. 2 The Wick Rotation10.2. 3 Scalar Massless Exchange in the Ladder Approximation&n 12.3 The Effective Action at the One-Loop Order12.3. 1 General Form12.3. 2 Two-Point Function12.3. 3 Other Functions12.3. 4 One-Loop Renormalization 12.4 Renormalization12.4. 1 Slavnov-Taylor Identities12.4. 2 Identities for Proper Functions12.4. 3 Recursive Construction of the Counterterms12.4. 4 Gauge Dependence of Green Functions12.4. 5 Anomalies 12.5 Massive Gauge Fields12.5. 1 Historical Background12.5. 2 Massive Gauge Theory12.5. 3 Spontaneous Symmetry Breaking12.5. 4 Renormalization of Spontaneously Broken Gauge12.5. 5 Gauge Independence and Unitarity of the S Matrix 12.6 The Weinberg-Salam Model12.6. 1 The Model for Leptons12.6. 2 Electron-Neutrino Cross Sections12.6. 3 Higher-Order Corrections12.6. 4 Incorporation of Hadrons13. Asymptotic Behavior 13.1 Effective Charge in Electrodynamics13.1. 1 The Gell-Mann and Low Function13.1. 2 The Callan-Symanzik Equation 13.2 Broken Scale Invariance13.2. 1 Scale and Conformal Invariance13.2. 2 Modified Ward Identities13.2. 3 Callan-Symanzik Coefficients to Lowest Order 13.3 Scale Invariance Recovered13.3. 1 Coupling Constant Flow13.3. 2 Asymptotic Freedom13.3. 3 Mass Corrections 13.4 Deep Inelastic Lepton-Hadron Scattering and Electron-Positron Annihilation into Hadrons13.4. 1 Electroproduction13.4. 2 Light-Cone Dynamics13.4. 3 Electron-Positron Annihilation 13.5 Operator Product Expansions13.5. 1 Short-Distance Expansion13.5. 2 Dominant and Subdominant Operators, Operator Mixing, and Conservation Laws13.5. 3 Light-Cone ExpansionAppendixA-1 MetricA-2 Dirac Matrices and SpinorsA-3 Normalization of States, S Matrix, Unitarity, and Cross SectionsA-4 Feynman RulesIndex