In this textbook for graduate students in physics the author carefully analyses the role of causality in Quantum Electrodynamics. This new approach makes it possible to give full proofs and carry out the detailed calculations of scattering processes in a mathematically rigorous manner. The book begins with Dirac's theory, followed by the quantum theory of free fields, including a new approach to the external field problem. Chapter 3 is devoted to causal perturbation theory, a powerful method that avoids ultraviolet divergences and solves the infrared problem by means of the adiabatic limit. Chapter 4 is concerned with general properties of the S matrix, such as renormalizability, gauge invariance, and unitarity. The renormalization group and interacting fields are also discussed. In Chapter 5 other electrodynamic couplings are considered. The extension of the methods to non-abelian gauge theories is briefly described. This new edition is partially rewritten and contains two new chapters.

Inhalt

0. Preliminaries.- 0.0 Historical Introduction.- 0.1 Minkowski Space and the Lorentz Group.- 0.2 Tensors in Minkowski Space.- 0.3 Some Topics of Scattering Theory.- 0.4 Problems.- 1. Relativistic Quantum Mechanics.- 1.1 Spinor Representations of the Lorentz Group.- 1.2 Invariant Field Equations.- 1.3 Algebraic Properties of the Dirac Equation.- 1.4 Discussion of the Free Dirac Equation.- 1.5 Gauge Invariance and Electromagnetic Fields.- 1.6 The Hydrogen Atom.- 1.7 Problems.- 2. Field Quantization.- 2.1 Second Quantization in Fock Space.- 2.2 Quantization of the Dirac Field.- 2.3 Discussion of the Commutation Functions.- 2.4 The Scattering Operator (S-Matrix) in Fock Space.- 2.5 Perturbation Theory.- 2.6 Electron Scattering.- 2.7 Pair Production.- 2.8 The Causal Phase of the S-Matrix.- 2.9 Non-Perturbative Construction of the Causal Phase.- 2.10 Vacuum Polarization.- 2.11 Quantization of the Radiation Field.- 2.12 Problems.- 3. Causal Perturbation Theory.- 3.1 The Method of Epstein and Glaser.- 3.2 Splitting of Causal Distributions.- 3.3 Application to QED.- 3.4 Electron Scattering (Moeller Scattering).- 3.5 Electron-Photon Scattering (Compton Scattering).- 3.6 Vacuum Polarization.- 3.7 Self-Energy.- 3.8 Vertex Function: Causal Distribution.- 3.9 Vertex Function: Retarded Distribution.- 3.10 Form Factors.- 3.11 Adiabatic Limit.- 3.12 Charged Particles in Perturbative QED.- 3.13 Charge Normalization.- 3.14 Problems.- 4. Properties of the S-Matrix.- 4.1 Vacuum Graphs.- 4.2 Operator Character of the S-Matrix.- 4.3 Normalizability of QED.- 4.4 Discrete Symmetries.- 4.5 Poincaré Covariance.- 4.6 Gauge Invariance and Ward Identities.- 4.7 Unitarity.- 4.8 Renormalization Group.- 4.9 Interacting Fields and Operator Products.- 4.10 Field Equations.- 4.11 Problems.- 5. Other Electromagnetic Couplings.- 5.1 Scalar QED: Basic Properties.- 5.2 Scalar QED: Gauge Invariance.- 5.3 Axial Anomalies.- 5.4 (2+1)-Dimensional QED: Vacuum Polarization.- 5.5 (2+1)-Dimensional QED: Mass Generation.- 5.6 Problems.- 6. Epilogue: Non-Abelian Gauge Theories.- Appendices.- A: The Hydrogen Atom According to the Schrödinger Equation.- B: Regularly Varying Functions.- C: Spence Functions.- D: Grassmann Test Functions.- Bibliographical Notes.