Scharf G. Finite Quantum Electrodynamics. The Causal Approach

Springer, 1995. — 410 p. — (Theoretical and Mathematical Physics). — ISBN: 978-3-642-63345-4; 978-3-642-57750-5.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.Preliminaries
Historical Introduction
Minkowski Space and the Lorentz Group
Tensors in Minkowski Space
Some Topics of Scattering Theory
Problems
Relativistic Quantum Mechanics
Spinor Representations of the Lorentz Group
Invariant Field Equations
Algebraic Properties of the Dirac Equation
Discussion of the Free Dirac Equation
Gauge Invariance and Electromagnetic Fields
The Hydrogen Atom
Problems
Field Quantization
Second Quantization in Fock Space
Quantization of the Dirac Field
Discussion of the Commutation Functions
The Scattering Operator (S-Matrix) in Fock Space
Perturbation Theory
Electron Scattering
Pair Production
The Causal Phase of the S-Matrix
Non-Perturbative Construction of the Causal Phase
Vacuum Polarization
Quantization of the Radiation Field
Problems
Causal Perturbation Theory
The Method of Epstein and Glaser
Splitting of Causal Distributions
Application to QED
Electron Scattering (Moeller Scattering)
Electron-Photon Scattering (Compton Scattering)
Vacuum Polarization
Self-Energy
Vertex Function: Causal Distribution
Vertex Function: Retarded Distribution
Form Factors
Adiabatic Limit
Charged Particles in Perturbative QED
Charge Normalization
Problems
Properties of the S-Matrix
Vacuum Graphs
Operator Character of the S-Matrix
Normalizability of QED
Discrete Symmetries
Poincare Covariance
Gauge Invariance and Ward Identities
Unitarity
Renormalization Group
Interacting Fields and Operator Products
Field Equations
Problems
Other Electromagnetic Couplings
Scalar QED: Basic Properties
Scalar QED: Gauge Invariance
Axial Anomalies
(2+1)-Dimensional QED: Vacuum Polarization
(2+1)-Dimensional QED: Mass Generation
Problems
Epilogue: Non-Abelian Gauge Theories
Appendices
The Hydrogen Atom According to the Schrodinger Equation
Regularly Varying Functions
Spence Functions
Grassmann Test Functions