The Heisenberg-Wigner formalism for transverse fields

TL;DR

This paper develops a phase-space formalism for transverse fields in quantum electrodynamics, deriving modified transport equations and simplifying momentum derivatives for better analysis of such fields.

Contribution

It introduces a tailored Heisenberg-Wigner formalism for transverse fields, including new transport equations and techniques to handle spatially oscillating fields.

Findings

Derived modified transport equations for transverse fields.

Simplified momentum derivative operators in oscillating fields.

Provided a framework for analyzing particle dynamics in specific electromagnetic configurations.

Abstract

We discuss the Heisenberg-Wigner phase-space formalism in quantum electrodynamics as well as scalar quantum electrodynamics with respect to transverse fields. In regard to the special characteristics of such field types we derive modified transport equations such that particle momenta perpendicular to the propagation direction of the waves show up as external parameters only. In case of spatially oscillating fields we further demonstrate how to transform momentum derivative operators of infinite order into simple coupling terms.