ar X iv : h ep - l at / 0 50 10 16 v 2 2 F eb 2 00 5 Curci - Ferrari mass and the Neuberger problem

We study the massive Curci-Ferrari model as a starting point for defining BRST quantisation for Yang-Mills theory on the lattice. In particular, we elucidate this proposal in light of topological approaches to gauge-fixing and study the case of a simple one-link Abelian model. BRST symmetry has proven an invaluable tool in the perturbative quantisa-tion of gauge theories [1] so that its elevation to the non-perturbative level is clearly desirable. For one, BRST methods are crucial in the formulation of Schwinger-Dyson equations (SDEs) in covariant gauges, which seem genuinely non-perturbative, have been subject to study using various truncations at this level[2], and whose results are now subject to comparisons with corresponding computations in Landau gauge from lattice gauge theory (see, for example, [3]). However, it has been demonstrated that a standard formulation of BRST symmetry invoked for lattice fields rigorously forces the partition function and path integrals of BRST invariant operators with a BRST invariant measure to vanish identically [4]. Rather than defining the configuration space in terms of some subset with no Gribov copies [5,6], one sums them all with alternating sign of the Faddeev-Popov determinant (only for small fields about A µ = 0 is this positive and thus the Jacobian of a change of variables) and a complete cancellation takes place giving the nonsensical result