  Electromagnetic fields of a massless charged particle are described by a
gauge potential that is almost everywhere pure gauge. Solution of quantum
mechanical wave equations in the presence of such fields is therefore immediate
and leads to a new derivation of the quantum electrodynamical eikonal
approximation. The elctromagnetic action in the eikonal limit is localised on a
contour in a two-dimensional Minkowski subspace of four-dimensional space-time.
The exact S-matrix of this reduced theory coincides with the eikonal
approximation, and represents the generalisatin to electrodynamics of the
approach of 't Hooft and the Verlinde's to Planckian scattering.
