Plane Wave Backgrounds in the Worldline Formalism

TL;DR

This paper introduces a new non-perturbative method within the worldline formalism to analyze QED in plane wave backgrounds, potentially simplifying complex calculations in strong-field quantum electrodynamics.

Contribution

It extends the worldline approach to plane wave backgrounds using resummation techniques, providing master formulas for effective action and scattering amplitudes.

Findings

Developed a non-perturbative resummation method for plane wave backgrounds.

Derived master formulas for effective action and scattering amplitudes.

Potential to streamline complex QED calculations in plane wave fields.

Abstract

Plane-wave backgrounds play a special role in strong-field QED as examples of a non-trivial field configuration that remains simple enough to be treated analytically whilst still leading to rich physical consequences. Although great progress has been made applying standard field theory techniques to QED in plane wave backgrounds, the calculations tend to be quite long and complicated. Yet, both in vacuum and in constant backgrounds, the first quantised, string-inspired "Worldline Approach" to field theory has a long history of offering substantial simplifications and calculational efficiency. We present a new, general approach to incorporating plane wave backgrounds into the Worldline Formalism that extends initial work using a semi-classical approach by Ilderton and Torgrimsson (who also participated in LPHYS'21). The method uses resummation techniques to take the background into account non-perturbatively and yields "Master Formulae" for the effective action and scattering amplitudes in the background. It is hoped that this may offer an alternative tool to studying QED in plane waves that may streamline otherwise complex calculations, as has been achieved in the better explored constant field case.