A few remarks on the zero modes of the Faddeev-Popov operator in the Landau and maximal Abelian gauges

TL;DR

This paper constructs explicit examples of normalizable zero modes of the Faddeev-Popov operator in Landau and maximal Abelian gauges for SU(2) Yang-Mills theories in three dimensions, demonstrating finite-norm gauge configurations.

Contribution

It provides explicit constructions of zero modes with finite norm in Landau and maximal Abelian gauges, advancing understanding of gauge fixing ambiguities.

Findings

Explicit infinite class of zero modes in Landau gauge

Finite norm gauge configurations constructed

Enhances understanding of gauge fixing in Yang-Mills theories

Abstract

The construction outlined by Henyey is employed to provide examples of normalizable zero modes of the Faddeev-Popov operator in the Landau and maximal Abelian gauges in SU(2) Euclidean Yang-Mills theories in d=3 dimensions. The corresponding gauge configurations have all finite norm ||A||^2 < \infty. In particular, in the case of the Landau gauge, the explicit construction of an infinite class of normalizable zero modes with finite norm ||A||^2 is provided.