Scattering in strong field QED in a nonnull background

We examine scattering amplitudes for an arbitrary number of photons in a class of nonnull background electromagnetic fields, studying tree-level and one-loop amplitudes in scalar and spinor quantum-electrodynamics in backgrounds defined by a gauge field A μ ( n · x ) for n 2 ≠ 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 formulas for the N -photon amplitudes dressed by the nonnull background are constructed using the first-quantized worldline formalism, which can systematically account for all orders in the nonnull parameter, 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 nonnull background nonperturbatively. We then outline a partial resummation of their expansions in n 2 . A special exactly solvable case of nonnull constant crossed fields without photon insertion in the effective action is explored to test the master formulas that result. The validity of the presented master formulas is further checked against known expressions for the wave function and nonlinear Compton scattering in a nonnull background to lowest order in the nonnull parameter.