Regularization of the Light-Cone Gauge Gluon Propagator Singularities Using Sub-Gauge Conditions

TL;DR

This paper investigates sub-gauge conditions in the light-cone gauge to regularize gluon propagator singularities in perturbative QCD, deriving conditions for known regularizations and verifying them through classical field calculations.

Contribution

It derives and verifies sub-gauge conditions for the principal value regularization of the gluon propagator in light-cone gauge, expanding understanding of gauge fixing in QCD.

Findings

Derived sub-gauge condition for PV regularization.

Verified the sub-gauge condition with classical Yang-Mills field calculation.

Identified limitations regarding the Mandelstam-Leibbrandt prescription.

Abstract

Perturbative QCD calculations in the light-cone gauge have long suffered from the ambiguity associated with the regularization of the poles in the gluon propagator. In this work we study sub-gauge conditions within the light-cone gauge corresponding to several known ways of regulating the gluon propagator. Using the functional integral calculation of the gluon propagator, we rederive the known sub-gauge conditions for the theta-function gauges and identify the sub-gauge condition for the principal value (PV) regularization of the gluon propagator's light-cone poles. The obtained sub-gauge condition for the PV case is further verified by a sample calculation of the classical Yang-Mills field of two collinear ultrarelativistic point color charges. Our method does not allow one to construct a sub-gauge condition corresponding to the well-known Mandelstam-Leibbrandt prescription for regulating the gluon propagator poles.