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

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.)