Worldline modeling of ultra-intense lasers for <i>N</i>-photon scattering processes

The modeling of present and future ultra-intense lasers demands techniques that go beyond the standard diagrammatic approach to non-perturbatively fully capture the effects of strong fields. We illustrate the first-quantized path integral representation for strong-field quantum electrodynamics as a means of accessing the laser being treated as a background field, which is treated without recourse to perturbation theory. We examine an all-multiplicity construction for N-photon scattering processes for complex scalars and spinors, showing compact Master Formulae for tree-level scattering. Several background fields are considered, including plane waves, impulsive parallel propagation waves, non-null fields, and homogeneous fields (constant-crossed fields) with low-energy external photons.