Introduction to bound-state quantum electrodynamics

Abstract

In this chapter we describe the fundamental aspects of bound-state quantum electrodynamics (BSQED).We recall the principal features of the Dirac equation. Then we describe quantum electrodynamics as a field theory. We provide the basic elements about representations, evolution operators and the S matrix. We then proceed to describe perturbation expansion of the S-matrix, and its relations with bound-state energies. We express this expansion in terms of Feynman diagrams. Finally we illustrate on practical examples the concepts of regularization, using the method of Pauli and Villars, and renormalization in coordinate space. We describe in detail the practical ways of doing the calculations, using self-energy, vacuum polarization, self-energy screening and QED corrections to the ladder approximation. Finally we show the quality of the agreement between BSQED and experiment by showing comparison for twoand three-electron ions transitions.