Heat-bath for the lattice Dirac propagator and a test of a Monte Carlo method for dynamical fermions

We describe a heat-bath method for inverting a non-hermitian matrix which is suitable for calculating the lattice Dirac propagator G(U) = [m + D(U)]^-1 in an arbitrary gluon field U. The method is a generalization of the usual heat-bath method for generating a gaussian distribution N exp[- 1 2xAx] from which the inverse (A)_β^-1 of the matrix A is easily obtained, provided A is a positive symmetric matrix. The new method is applied in the Monte Carlo method for dynamical fermions previously developed by the authors, after the ratio of fermionic determinants, which is required for gluon updating, has been expressed in terms of the lattice Dirac propagator. As a test of the present approach, we performed numerical calculations in the U(1) lattice gauge theory with dynamical fermions (lattice QED) and compared them to the very accurate results which are available from the dimer method at β = g^-2 = 0.