Equivariant Gauge Fixing of SU ( 2 ) Lattice Gauge Theory

I construct a Lattice Gauge Theory (LGT) with discrete Z2 structure group and an equivariant BRST symmetry that for gauge invariant observables is equivalent to the standard SU(2)-LGT. The measure of this Z2-LGT is invariant under all the discrete symmetries of the lattice. The SU(2) structure group of the original LGT is first reduced to an U(1) structure group by an equivariant BRST construction. In a second step this abelian LGT is shown to be physically equivalent to a model with only a discrete Z2 gauge invariance. The Topological Lattice Theories (TLT) that localize on the moduli spaces of these models are constructed and their BRST symmetry is exhibited. The method can be generalized to obtain a covariant LGT with gauge group Zn and an equivariant BRST symmetry that is physically equivalent to an SU(n) LGT. The Grassmann variables of the Z2-invariant local LGT and most of the additional local bosonic fields are explicitly integrated in favor of a nonlocal bosonic measure. In addition to the SU(2) link variables and the coupling g2, the measure of this Z2 LGT also depends on an auxiliary (gauge invariant) site variable of canonical dimension two and on a gauge parameter α. The maximum of the bosonic measure in the thermodynamic limit for a lattice