N-photon amplitudes in a plane-wave background

TL;DR

This paper derives master formulas for one-loop N-photon amplitudes in a plane-wave background using the worldline formalism, extending previous work and revealing a crypto-gaussian structure specific to this background.

Contribution

It introduces a novel application of the worldline formalism to compute N-photon amplitudes in plane-wave backgrounds, generalizing prior vacuum polarisation results.

Findings

Derived master formulas for scalar and spinor QED amplitudes.

Uncovered the crypto-gaussian nature of the worldline path integral in this context.

Extended previous vacuum polarisation work to more general N-photon processes.

Abstract

We use the worldline formalism to derive master formulas for the one-loop N-photon amplitudes in a plane-wave background, for both scalar and spinor QED. This generalises previous work by Ilderton and Torgrimsson for the vacuum polarisation case, although with some change in methodology since, instead of evaluating the path integral on the semi-classical trajectory, we use the special kinematics of the plane-wave background to uncover the crypto-gaussian character of this type of worldline path integral.