  We discuss the Heisenberg-Wigner phase-space formalism in quantum
electrodynamics as well as scalar quantum electrodynamics with respect to
transverse fields. In regard to the special characteristics of such field types
we derive modified transport equations such that particle momenta perpendicular
to the propagation direction of the waves show up as external parameters only.
In case of spatially oscillating fields we further demonstrate how to transform
momentum derivative operators of infinite order into simple coupling terms.
