Electromagnetic fields of a massless particle and the eikonal

TL;DR

This paper explores the electromagnetic fields of massless charged particles, deriving a localised action in the eikonal limit and connecting it to quantum electrodynamics and high-energy scattering theories.

Contribution

It introduces a new derivation of the quantum electrodynamical eikonal approximation using the gauge potential of massless particles and links it to Planckian scattering approaches.

Findings

Electromagnetic fields of massless particles are almost pure gauge.

The eikonal limit action is localized on a contour in Minkowski space.

The S-matrix in this limit matches the eikonal approximation and generalizes high-energy scattering theories.

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.