Expectation values of Coherent States for ${\rm SU}(2)$ Lattice Gauge Theories

TL;DR

This paper analyzes the expectation values of semiclassical coherent states in SU(2) lattice gauge theories, providing explicit calculations of quantum corrections and insights into quantum fluctuations in non-abelian gauge systems.

Contribution

It explicitly computes expectation values and quantum corrections for SU(2) coherent states, advancing understanding of semiclassical properties in non-abelian lattice gauge theories.

Findings

Explicit expectation values for SU(2) coherent states

First-order quantum corrections calculated

Enhanced understanding of quantum fluctuations

Abstract

This article investigates properties of semiclassical Gauge Field Theory Coherent States for general quantum gauge theories. Useful, e.g., for the canonical formulation of Lattice Gauge Theories these states are labelled by a point in the classical phase space and constructed such that the expectation values of the canonical operators are sharply peaked on said phase space point. For the case of the non-abelian gauge group SU(2), we will explicitly compute the expectation value of general polynomials including the first order quantum corrections. This allows asking more precise questions about the quantum fluctuations of any given semiclassical system.