Mode truncations and scattering in strong fields

Truncating quantum field theories to a dominant mode offers a non-perturbative approach to their solution. We consider here the interaction of charged scalar matter with a single mode of the electromagnetic field. The implied breaking of explicit Lorentz invariance prompts us to compare instant-form quantisation and front-form, with the latter yielding significant simplifications when light-front zero modes are included. Using these field theory results we reassess the validity of existing first-quantised approaches to depletion effects in strong laser fields, and propose an alternative interpretation based on the dressing approach to QED and its infra-red structure.