Coherent states, Yang-Mills theory, and reduction

TL;DR

This paper discusses the canonical quantization of Yang-Mills theory on a spacetime cylinder, highlighting how gauge symmetry influences the Segal-Bargmann transform for compact groups.

Contribution

It introduces a method to derive the generalized Segal-Bargmann transform from the ordinary one by imposing gauge symmetry, advancing the understanding of quantization in gauge theories.

Findings

Connection between gauge symmetry and Segal-Bargmann transform

Framework for quantizing Yang-Mills theory on a cylinder

Insights into the role of coherent states in gauge theories

Abstract

This paper explains some of the ideas behind a prior joint work of the author with Bruce Driver on the canonical quantization of Yang-Mills theory on a spacetime cylinder. The idea is that the generalized Segal-Bargmann transform for a compact group can be obtained from the ordinary Segal-Bargmann transform by imposing gauge symmetry.