Worldline Modeling of Ultra-Intense Lasers for N-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 considering including: plane waves, impulsive PP-waves, non-null fields, and homogeneous fields (constant-crossed fields) with low-energy external photons.