Quantum Electrodynamics of Weak Fields

Abstract

Two ways of presenting ordinary quantum electrodynamics of weak fields exist. The first, more formal in nature, starts with the quantization of wave fields; the second, more easily dealt with, stems from Stückelberg and Feynman [St 41, Fe 48] and uses propagator techniques. We shall review here in condensed form this second approach and apply it to scattering processes. It is our goal to derive formulas for transition probabilities and scattering processes within the quantized version of Dirac’s hole theory for electrons and positrons. These calculations are in principle exact, but in practice use perturbation theory. Since creation and annihilation processes of electron — positron pairs have to be dealt with in the formalism, it must necessarily be relativistic.