Gauge-Invariant Variables and Mandelstam Constraints in SU(2) Gauge Theory

TL;DR

This paper reviews a solution to Mandelstam constraints in SU(2) gauge theory, enabling a complete description of physical configurations using gauge-invariant variables, simplifying the understanding of lattice gauge theories.

Contribution

It presents a novel, simplified solution to Mandelstam constraints for SU(2), highlighting the role of discrete gauge-invariant variables in describing physical states.

Findings

Complete description of SU(2) gauge configurations using gauge-invariant variables

Simplification of the Mandelstam constraints

Emphasis on the role of discrete variables in gauge theories

Abstract

The recent solution of the Mandelstam constraints for SU(2) is reviewed. This enables the subspace of physical configurations of an SU(2) pure gauge theory on the lattice (introduced solely to regulate the number of fields) with 3N physical degrees of freedom to be fully described in terms of 3N gauge-invariant continuous loop variables and N-1 gauge-invariant discrete +/-1 variables. The conceptual simplicity of the solution and the essential role of the discrete variables are emphasized. (Talk presented at QCD '94, Montpellier, France, 7-13 July 1994.)