Electromagnetic fields of a massless particle and the eikonal

Abstract

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.

The missing overdot -- signifying the $\tau$ differentiation ${\nabla }^2{\dot{\Omega }}^{+-}and{\dot{k}}^{+-}$ in eqs. (23) and (24) -- is inserted. Also, obsolete macro has been fixed. Plain TeX, 13 pages

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