The Configuration Space of Low-dimensional Yang-Mills Theories

TL;DR

This paper explores the structure of the configuration space in low-dimensional Yang-Mills theories, comparing gauge fixing and gauge invariant methods, and clarifies the role of Gribov ambiguities and non-generic configurations.

Contribution

It demonstrates the equivalence of gauge fixing and gauge invariant approaches in constructing the physical configuration space when properly handling the Gribov problem.

Findings

Gauge fixing and gauge invariant methods are equivalent with proper Gribov treatment.

Proper boundary identifications resolve Gribov ambiguities.

Non-generic configurations are significant in the configuration space.

Abstract

We discuss the construction of the physical configuration space for Yang-Mills quantum mechanics and Yang-Mills theory on a cylinder. We explicitly eliminate the redundant degrees of freedom by either fixing a gauge or introducing gauge invariant variables. Both methods are shown to be equivalent if the Gribov problem is treated properly and the necessary boundary identifications on the Gribov horizon are performed. In addition, we analyze the significance of non-generic configurations and clarify the relation between the Gribov problem and coordinate singularities.