Coherent states in gauge theories: Topological defects and other classical configurations

We present a formulation of coherent states as of consistent quantum description of classical configurations in the Becchi-Rouet-Stora-Tyutin (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 nontrivial configurations in gauge theories and makes a 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 reparametrizations in general relativity.