Classical and quantum particle dynamics in univariate background fields

TL;DR

This paper explores how classical and quantum charged particle dynamics deviate from the plane wave model in strong electromagnetic fields, highlighting the loss of integrability and the effectiveness of WKB approximations.

Contribution

It provides a detailed analysis of classical and quantum deviations from the plane wave model, especially in non-lightlike backgrounds, and evaluates approximation methods.

Findings

Radiation spectrum in spacelike fields approximates plane wave results at high energy.

WKB and uniform-WKB methods yield good approximations across cases.

Simplified differential equation approaches can miss key physics in barrier and scattering scenarios.

Abstract

We investigate deviations from the plane wave model in the interaction of charged particles with strong electromagnetic fields. A general result is that integrability of the dynamics is lost when going from lightlike to timelike or spacelike field dependence. For a special scenario in the classical regime we show how the radiation spectrum in the spacelike (undulator) case becomes well-approximated by the plane wave model in the high energy limit, despite the two systems being Lorentz inequivalent. In the quantum problem, there is no analogue of the WKB-exact Volkov solution. Nevertheless, WKB and uniform-WKB approaches give good approximations in all cases considered. Other approaches that reduce the underlying differential equations from second to first order are found to miss the correct physics for situations corresponding to barrier transmission and wide-angle scattering.