Asymptotic states in quantum electrodynamics

Abstract

The time evolution of a system of charged particles due to the long-range part of the Coulomb interaction and the interaction with the soft part of the transverse radiation field is studied within the frame-work of frist-quantized theory of the charged particles and second-quantized theory of the electromagnetic field. States are defined which may serve as asymptotic states in a scattering theory. They differ from the free states by a phase factor (generalization of the Coulomb phase) and by the presence of a coherent soft radiation field. The time development of the phase factor and of the wave function that describes the coherent field is studied in detail and expressed in terms of elementary functions. An outline is made of an S-matrix theory based on the asymptotic states thus defined.