Renormalization of Yang-Mills fields in the light-front without non-local terms

TL;DR

This paper addresses the renormalization of Yang-Mills fields in the light-front gauge by correcting the gauge fixing procedure, resulting in a local vacuum polarization tensor at one-loop level without non-local divergences.

Contribution

It identifies a deficiency in the gauge fixing procedure and proposes a corrected propagator that eliminates non-local divergent terms in light-front Yang-Mills renormalization.

Findings

Corrected propagator removes non-local divergences

Vacuum polarization tensor is local at one-loop level

Provides a consistent renormalization approach in light-front gauge

Abstract

The study of renormalization of Yang-Mills fields in the light-front gauge has always been a delicate subject in that divergent {\em non-local} terms arise from the calculations of Feynman diagrams. In this short paper we show that this happened because of a deficiency in the gauge fixing procedure that results in an incorrect propagator and propose a cure for it by considering the {\em correct} propagator for the gauge potential. We explicitly show that the use of our correct propagator in the light-front leads to a vacuum polarization tensor at the one-loop level that is free of non-local terms.