One-loop vertex correction in a plane wave

TL;DR

This paper derives the one-loop vertex correction in a general plane-wave background, analyzing its properties, divergences, and behavior in high-field regimes, with implications for quantum electrodynamics in intense fields.

Contribution

It provides a general expression for the one-loop vertex correction in arbitrary plane-wave backgrounds, including divergence analysis and high-field asymptotics.

Findings

Infrared divergence cured by photon mass assignment

Ultraviolet divergence renormalized as in vacuum

High-field asymptotic scales according to Ritus-Narozhny conjecture

Abstract

We compute the general expression of the one-loop vertex correction in an arbitrary plane-wave background field for the case of two on-shell external electrons and an off-shell external photon. The properties of the vertex corrections under gauge transformations of the plane-wave background field and of the radiation field are studied. Concerning the divergences of the vertex correction, the infrared one is cured by assigning a finite mass to the photon, whereas the ultraviolet one is shown to be renormalized exactly as in vacuum. Finally, the corresponding expression of the vertex correction within the locally-constant crossed field is also derived and the high-field asymptotic is shown to scale according to the Ritus-Narozhny conjecture.