BRST Inner Product Spaces and the Gribov Obstruction

TL;DR

This paper explores extending the BRST inner product to gauge theories with complex gauge orbits, identifying cases where it succeeds or fails due to the Gribov obstruction, and discusses potential solutions.

Contribution

It extends the Batalin-Marnelius proposal to a broader class of gauge theories, analyzing conditions for successful global extension and the impact of the Gribov obstruction.

Findings

The adapted method applies to many mechanical models with semisimple gauge groups.

Some models exhibit a Gribov obstruction preventing a global inner product extension.

Partial success and failure are explained, with brief discussions on possible remedies.

Abstract

A global extension of the Batalin-Marnelius proposal for a BRST inner product to gauge theories with topologically nontrivial gauge orbits is discussed. It is shown that their (appropriately adapted) method is applicable to a large class of mechanical models with a semisimple gauge group in the adjoint and fundamental representation. This includes cases where the Faddeev-Popov method fails. Simple models are found also, however, which do not allow for a well-defined global extension of the Batalin-Marnelius inner product due to a Gribov obstruction. Reasons for the partial success and failure are worked out and possible ways to circumvent the problem are briefly discussed.