Master formulas for the dressed scalar propagator in a constant field

TL;DR

This paper extends the worldline formalism to derive a master formula for the dressed scalar propagator in a constant external field, enabling efficient computation of Compton scattering cross sections across various field strengths.

Contribution

It introduces a new master formula for the scalar propagator in a constant field, expanding previous vacuum formulas to include external field effects.

Findings

Derived an integral representation for the Compton scattering cross section in a constant field.

Extended the scalar QED master formula to incorporate constant external fields.

Provided a framework suitable for numerical evaluation across all field strengths.

Abstract

The worldline formalism has previously been used for deriving compact master formulas for the one-loop N-photon amplitudes in both scalar and spinor QED, and in the vacuum as well as in a constant external field. For scalar QED, there is also an analogous master formula for the propagator dressed with N photons in the vacuum. Here, we extend this master formula to include a constant field. The two-photon case is worked out explicitly, yielding an integral representation for the Compton scattering cross section in the field suitable for numerical integration in the full range of electric and magnetic field strengths.