Eur. Phys. J. C (2016) 76: 243
https://doi.org/10.1140/epjc/s10052-016-4075-z

Regular Article - Theoretical Physics

Absence of the Gribov ambiguity in a quadratic gauge

Department of Physics, Indian Institute of Technology, Bombay, Mumbai, 400076, India

^* e-mail: haresh@phy.iitb.ac.in
^** e-mail: haresh.ein@gmail.com

Received: 21 January 2016
Accepted: 11 April 2016
Published online: 30 April 2016

Abstract

The Gribov ambiguity exists in various gauges. Algebraic gauges are likely to be ambiguity free. 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 , when a proper boundary condition on the gauge configuration is taken into account. Thus, we provide one example where the ambiguity is absent on a compact manifold in the algebraic gauge. We also show that the BRST invariance is preserved in this gauge.