  Exploiting the gauge freedom associated with the Volkov description of a
charge propagating in a plane wave background, we identify a new type of gauge
choice which significantly simplifies the theory. This allows us to develop a
compact description of the propagator for both scalar and fermionic matter, in
a circularly polarised background. It is shown that many of the usually
observed structures are gauge artefacts. We then analyse the full ultraviolet
behaviour of the one-loop corrections for such charges. This enables us to
identify and contrast the different renormalisation prescriptions needed for
both types of matter.
