Master formulas for photon amplitudes in a combined constant and plane-wave background field

TL;DR

This paper extends the worldline formalism to derive compact master formulas for scalar and spinor QED N-photon amplitudes in a combined constant and plane-wave background field, focusing on a special parallel case.

Contribution

It introduces new master formulas for QED photon amplitudes in a combined background, advancing the understanding of quantum electrodynamics in complex fields.

Findings

Derived master formulas for scalar and spinor QED in combined fields

Extended the worldline formalism to a new class of background fields

Provided a framework for future calculations in complex electromagnetic backgrounds

Abstract

The worldline formalism has previously been used for deriving compact master formulas for the QED $N$ - photon amplitudes in vacuum, in a constant field and in a plane-wave field. Here we carry this program one step further by deriving master formulas for the scalar and spinor QED $N$-photon amplitudes in the background of the "parallel" special case of a combined constant and plane-wave field.