In this book the author carefully analyses the role of the concept of causality in Quantum Electrodynamics. This approach makes it possible for the first time to publish a textbook on QED which not only includes full proofs and detailed calculations but is also mathematically rigorous. The book begins with Dirac's theory in part one, followed in part two by the quantum theory of free fields including a new approach to the concept of exterior fields. The third part is devoted to the study of the S-matrix of QED avoiding ultraviolet divergence. The most important physical results of QED are derived, and significant themes such as unitarity and renormalizability of the theory are discussed. This slim book addresses graduate students in physics. From the reviews: "In the summary on the back cover the unheard-of statement appears that now the first (mathematically) rigorous textbook on Quantum Electrodynamics was on hand. ... In fact, "Finite Quantum Electrodynamics" does justice to this claim. And, in addition, in a pregnant, lifely form. On 220 pages G. Scharf (Zurich) succeeds in presenting a concise description of QED ... As promised, only finite quantities appear ... In Russia I often feel frustrated that I studied Latin in school and Russian was not offered. Now I have the same feeling after reading Scharf's book. I studied the wrong grammar up to now." #Translated from a review by Thomas Schücker in Physik in unserer Zeit#1

Inhalt

0. Preliminaries.- 0.1 Minkowski Space and the Lorentz Group.- 0.2 Tensors in Minkowski Space.- 0.3 Some Topics of Scattering Theory.- 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.- 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.- 2.9 Non-Perturbative Construction of the Causal Phase.- 2.10 Vacuum Polarization.- 2.11 Quantization of the Radiation Field.- 3. Causal Perturbation Theory.- 3.1 The Method of Epstein and Glaser.- 3.2 Splitting of 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.- 3.9 Form Factors.- 3.10 Infrared Cancellations.- 3.11 Symmetry Properties of the S-Matrix.- 3.12 Normalizability of QED.- Appendix: Spence Functions.