A Non-Principal Value Prescription for the Temporal Gauge

TL;DR

This paper introduces a non-principal value prescription to handle singularities in Yang-Mills theory within the temporal gauge, providing explicit calculations and a regularization method for one-loop integrals.

Contribution

It presents a novel non-principal value prescription for temporal gauge singularities and demonstrates its effectiveness through explicit one-loop integral calculations.

Findings

Divergent parts are local and match those in the spatial axial gauge with principal-value prescription.

A regularization method for spurious gauge divergences is proposed.

The approach facilitates renormalization in the temporal gauge.

Abstract

A non-principal value prescription is used to define the spurious singularities of Yang-Mills theory in the temporal gauge. Typical one-loop dimensionally-regularized temporal-gauge integrals in the prescription are explicitly calculated, and a regularization for the spurious gauge divergences is introduced. The divergent part of the one-loop self-energy is shown to be local and has the same form as that in the spatial axial gauge with the principal-value prescription. The renormalization of the theory is also briefly mentioned.