OBTAINING A LIGHT-LIKE PLANAR GAUGE

Abstract

In the usual and current understanding of planar gauge choices for Abelian and non-Abelian gauge fields, the external defining vector nμ can either be space-like (n2 < 0) or time-like (n2>0) but not light-like (n2=0). In this work we propose a light-like planar gauge that consists of defining a modified gauge-fixing term, 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 nμ and its dual mμ, with n2=m2=0, n·m≠0, say, e.g. normalized to n·m=2.