Solution of the SU(2) Mandelstam Constraints

TL;DR

This paper presents a complete solution to the Mandelstam constraints in SU(2) lattice gauge theory, expressing the theory entirely in gauge-invariant variables, which simplifies analysis and computation.

Contribution

It introduces a method to solve the SU(2) Mandelstam constraints explicitly using Wilson, Polyakov loops, and discrete variables, enabling a gauge-invariant formulation.

Findings

Complete solution to SU(2) Mandelstam constraints

Expresses gauge theory in terms of gauge-invariant variables

Facilitates gauge-invariant analysis of lattice gauge theories

Abstract

It is shown how the Mandelstam constraints for an $SU(2)$ pure lattice gauge theory with $3{\cal N}$ physical degrees of freedom may be solved completely in terms of $3{\cal N}$ Wilson and Polyakov loop variables and ${\cal N}-1$ gauge invariant discrete +/-1 variables, thus enabling a manifestly gauge invariant formulation of the theory.