Consistent Perturbative Light Front Formulation of Yang-Mills Theories

TL;DR

This paper develops a consistent light front quantization method for Yang-Mills theories, overcoming previous difficulties by using the anti light cone gauge, and aligns the perturbative framework with conventional approaches.

Contribution

It introduces a consistent perturbative light front formulation of Yang-Mills theories using the anti light cone gauge, matching the standard instant form results.

Findings

The generating functional matches the conventional approach.

The Mandelstam-Leibbrandt prescription is derived for the gluon propagator.

The formulation overcomes previous gauge-related difficulties.

Abstract

It is shown how to obtain the consistent light front form quantization of a non-Abelian pure Yang-Mills theory (gluondynamics) in the framework of the standard perturbative approach. After a short review of the previous attempts in the light cone gauge $A_-=0$, it is explained how the difficulties can be overcome after turning to the anti light cone gauge $A_+=0$. In particular, the generating functional of the renormalized Green's functions turns out to be the same as in the conventional instant form approach, leading to the Mandelstam-Leibbrandt prescription for the free gluon propagator.