Description
We study low energy photons coupled to spinor matter in the presence of a homogeneous electromagnetic field with arbitrary field strength in a first-quantised (worldline) approach. Using a Fock-Schwinger gauge for both the scattering photons and homogeneous background field, simple compact expressions are found for both the photon- and background-dressed effective action and propagator in QED. The low-energy limit makes possible the identification of the coupling of the scattering photons as one of an effective homogeneous superposition of their field strengths, with amplitudes following from application of a suitable linearisation operator. We also discuss a novel worldline representation of the momentum space matter propagators, obtaining a suitable worldline Green function for this path integral satisfying homogeneous Dirichlet boundary conditions representing the scattering photons.
