Propagation in an intense background

The canonical quantisation of a charged particle in an intense laser background is developed and the associated two-point function calculated. It is shown how the causal propagator can be extracted. We provide an interpretation of this propagator in terms of degenerate quantum processes. The spectral properties of the propagator are derived and we show how multi-pole structures emerge as a perturbative feature. We also calculate the associated multiple wave-function renormalisations to all orders in perturbation theory. Our calculations are for both circular and linearly polarised plane wave laser backgrounds.