Perturbative Formulation of Pure Space-Like Axial Gauge QED with Infrared Divergences Regularized by Residual Gauge Fields

TL;DR

This paper develops a perturbative approach to pure space-like axial gauge QED that regularizes infrared divergences using residual gauge fields, enabling consistent calculations including the electron self energy in light-cone gauge.

Contribution

It introduces a new perturbative formulation of axial gauge QED with residual gauge fields to handle infrared divergences, and successfully computes the one-loop electron self energy in light-cone gauge.

Findings

Infrared divergences cancel between residual gauge fields and physical gauge fields.

The gauge field propagator matches Mandelstam-Leibbrandt prescription.

One-loop electron self energy calculated successfully in light-cone gauge.

Abstract

We construct a new perturbative formulation of pure space-like axial gauge QED in which the inherent infrared divergences are regularized by residual gauge fields. For that purpose we perform our calculations in coordinates $x^{\mu}=(x^+,x^-,x^1,x^2)$, where $x^+=x^0\sin{\theta}+x^3\cos {\theta}$ and $x^-=x^0\cos{\theta}-x^3\sin{\theta}$. $A_-=A^0\cos{\theta}+A^3 \sin{\theta}=n{\cdot}A=0$ is taken as the gauge fixing condition. We show in detail that, in perturbation theory, infrared divergences resulting from the residual gauge fields cancel infrared divergences resulting from the physical parts of the gauge field. As a result we obtain the gauge field propagator prescribed by Mandelstam and Leibbrandt. By taking the limit $\theta {\to} \frac{\pi}{4}$ we can construct the light-cone formulation which is free from infrared difficulty. With that analysis complete, we perform a successful calculation of the one loop electron self energy, something not previously done in light-cone quantization and light-cone gauge.