Obtaining a light-like planar gauge

TL;DR

This paper introduces a novel light-like planar gauge for gauge fields, utilizing null vectors to define a gauge-fixing term, which extends the current understanding of gauge choices beyond space-like and time-like options.

Contribution

It proposes a new light-like planar gauge using null vectors, enabling gauge fixing in scenarios where the defining vector is light-like, which was not previously possible.

Findings

Defines a gauge-fixing term with two light-like vectors

Breaks Lorentz covariance in a controlled manner

Extends gauge choice options to light-like vectors

Abstract

In the usual and current understanding of planar gauge choices for Abelian and non Abelian gauge fields, the external defining vector $n_\mu$ can either be space-like ($n^2<0$) or time-like ($n^2>0$) but not light-like ($n^2=0$). In this work we propose a light-like planar gauge that consists in defining a modified gauge-fixing term, $\cal{L}_{GF}$, whose main characteristic is a two-degree violation of Lorentz covariance arising from the fact that four-dimensional space-time spanned entirely by null vectors as basis necessitates two light-like vectors, namely $n_\mu$ and its dual $m_\mu$, with $n^2=m^2=0, n\cdot m\neq 0$, say, e.g. normalized to $n\cdot m=2$.