Coherent States in Null-Plane Q.E.D

TL;DR

This paper demonstrates that using a coherent state basis in light front QED calculations can eliminate true infrared divergences at lowest order, offering an alternative to mass regularization.

Contribution

It introduces a method to handle IR divergences in light front QED by employing a coherent state basis, avoiding the need for a small photon mass.

Findings

Transition matrix element is IR divergence free at O(e^2).

Coherent states effectively cancel true IR divergences in light cone QED.

Provides a model calculation for the three-point vertex correction.

Abstract

Light front field theories are known to have the usual infra-red divergences of the equal time theories, as wellas new `spurious' infra-red divergences. The formar kind of IR divergences are usually treated by giving a small mass to the gauge particle. An alternative method to deal with these divergences is to calculate the transition matrix elements in a coherent state basis. In this paper we present, as a model calculation the lowest order correction to the three point vertex in QED using a coherent state basis in the light cone formalism. The relevant transition matrix element is shown to be free of the true IR divergences up to $O(e^2)$.