Quantisation without Gauge Fixing: Avoiding Gribov Ambiguities through the Physical Projector

TL;DR

This paper introduces a gauge-invariant quantisation method using a physical projector to avoid Gribov ambiguities, demonstrated through a solvable U(1) model related to Yang-Mills theory.

Contribution

It proposes a novel gauge-invariant quantisation approach based on the physical projector, eliminating the need for gauge fixing and associated Gribov issues.

Findings

The method successfully avoids Gribov ambiguities.

Application to a solvable U(1) model demonstrates effectiveness.

Provides insights into non-perturbative phenomena in gauge theories.

Abstract

The quantisation of gauge invariant systems usually proceeds through some gauge fixing procedure of one type or another. Typically for most cases, such gauge fixings are plagued by Gribov ambiguities, while it is only for an admissible gauge fixing that the correct dynamical description of the system is represented, especially with regards to non perturbative phenomena. However, any gauge fixing procedure whatsoever may be avoided altogether, by using rather a recently proposed new approach based on the projection operator onto physical gauge invariant states only, which is necessarily free on any such issues. These different aspects of gauge invariant systems are explicitely analysed within a solvable U(1) gauge invariant quantum mechanical model related to the dimensional reduction of Yang-Mills theory.