Absence of the Gribov ambiguity in a quadratic gauge

Haresh Raval

doi:10.1140/epjc/s10052-016-4075-z

Haresh Raval

Open Access

https://doi.org/10.1140/epjc/s10052-016-4075-z

Copy DOI

Abstract

The Gribov ambiguity exists in various gauges except algebraic gauges. However, algebraic gauges are not Lorentz invariant, which is their fundamental flaw. In addition, they are not generally compatible with the boundary conditions on the gauge fields, which are needed to compactify the space i.e., the ambiguity continues to exist on a compact manifold. Here we discuss a quadratic gauge fixing, which is Lorentz invariant. We consider an example of a spherically symmetric gauge field configuration in which we prove that this Lorentz invariant gauge removes the ambiguity on a compact manifold $\mathbb{S}^3$, when a proper boundary condition on the gauge configuration is taken into account. Thus, providing one example where the ambiguity is absent on a compact manifold in the algebraic gauge. We also show that the \tmem{BRST} invariance is preserved in this gauge.

Highlights

An essential reason why some gauges have the ambiguity is the differential operator involved in the gauge
Algebraic gauges are likely to be ambiguity free since they do not have a differential operator, but they have one disadvantage. They violate the Lorentz invariance, which is a basic requirement for any theory, whereas the gauge under consideration in this paper is Lorentz invariant
We prove that when a proper boundary condition on the gauge configuration at ∞ is taken into account, the quadratic gauge uniquely chooses the configuration on a compact manifold S3

Summary

Introduction

An essential reason why some gauges have the ambiguity is the differential operator involved in the gauge. Algebraic gauges are likely to be ambiguity free since they do not have a differential operator, but they have one disadvantage. They violate the Lorentz invariance, which is a basic requirement for any theory, whereas the gauge under consideration in this paper is Lorentz invariant. [6,7] The former reference is an approach using Lorentz invariant algebraic gauge conditions. We prove that when a proper boundary condition on the gauge configuration at ∞ is taken into account, the quadratic gauge uniquely chooses the configuration on a compact manifold S3

A quadratic gauge and effective Lagrangian

Spherically symmetric gauge potential and the quadratic gauge

BRST symmetry in quadratic gauge