Coherent States in Gauge Theories: Topological Defects and Other Classical Configurations

TL;DR

This paper develops a BRST-invariant coherent state framework for gauge theories, enabling a quantum description of classical configurations, including topological defects like Nielsen-Olesen strings, enhancing understanding of topologically non-trivial sectors.

Contribution

It introduces a method to construct BRST-invariant coherent states for gauge theories, including pure-gauge and topological configurations, providing new insights into their quantum properties.

Findings

Constructed BRST-invariant coherent states for gauge configurations.

Demonstrated the approach with Nielsen-Olesen string example.

Showed suppression of transitions between topologically distinct sectors.

Abstract

We present a formulation of coherent states as of consistent quantum description of classical configurations in the BRST-invariant quantization of electrodynamics. The quantization with proper gauge-fixing is performed on the vacuum of the theory, whereas other backgrounds are obtained as BRST-invariant coherent states. One of the key insights is the possibility of constructing the coherent states of pure-gauge configurations. This provides a coherent state understanding of topologically non-trivial configurations in gauge theories, and makes number of features, such as the suppression of transitions between topologically-distinct sectors, very transparent at full quantum level. As an example, we construct the Nielsen-Olesen string as a BRST-invariant coherent state. The Abelian pure-gauge configurations can also be viewed as useful analogs for a set of space-times related by coordinate reparameterizations in General Relativity.