Scattering in strong field QED in a non-null background
We examine scattering amplitudes for an arbitrary number of photons in a class of non-null background electromagnetic fields, studying tree-level and one-loop amplitudes in scalar and spinor quantum-electrodynamics in backgrounds defined by a gauge field $A_{\mu}(\mathfrak{n}\cdot x)$ for $\mathfrak{n}^2\neq 0$. Motivated to account for more physically realistic laser-plasma dispersive properties, our approach overcomes prior work studying such amplitudes in a constant background field and relaxes the familiar null criterion assumed for plane waves. Master Formulae for the $N$-photon amplitudes dressed by the non-null background are constructed using the first-quantised worldline formalism, which can systematically account for all orders in the non-null parameter, $\mathfrak{n}^2$, treated here as an expansion parameter. These are derived from worldline representations of the coordinate and momentum space propagators (and their LSZ-truncated amplitudes) and the effective action, each incorporating the non-null background non-perturbatively. We then outline a partial resummation of their expansions in $\mathfrak{n}^{2}$. A special exactly solvable case of non-null constant crossed fields without photon insertion in the effective action is explored to test the Master Formulae that result. The validity of the presented master formulae is further checked against known expressions for the wavefunction and non-linear Compton scattering in a non-null background to lowest order in the non-null parameter.