Simulations with lattice QCD at finite density

A method proposed by Barbour, Davies and Sabeur is used to expand the grand canonical partition function for QCD on a finite lattice in terms of the canonical partition functions for a fixed number of fermions. We show how the lattice action corresponding to the canonical partition function for a given fermion number can be obtained. The method is not unique to QCD and can be applied to other theories with complex action. This expansion of the GCPF is used to study QCD at finite density. The results of preliminary numerical simulations performed on a 44 lattice are described. Evidence is found for the positivity and continuity of the canonical partition functions as a function of the fermion number. The number density shows a clear signal of a transition at a density (in lattice units) of about 0.35 at β=4.9 and small quark mass. (orig.)