The Microcanonical Fermionic Average Method for Monte Carlo Simulations of Lattice Gauge Theories with Dynamical Fermions

In this article we present a comprehensive exposition of a method for performing numerical simulations of lattice gauge theories with dynamical fermions. Its main aspects had been presented elsewhere. This work is a systematic study of the feasibility of the method, which amounts to separating the evaluation of the Fermionic Determinant from the generation of gauge configurations through a microcanonical process. The main advantage consists in the fact that the parts of the simulation which are most computer intensive must not be repeated when varying the parameters of the theory. Moreover we achieve good control over critical slowing down, since the configurations over which the determinant is measured are always very well decorrelated; in addition, the actual implementation of the method allows us to perform simulations at exactly zero fermion mass. We relate the numerical feasibility of this approach to an expansion in the number of flavours; the criteria for its convergence are analyzed both theoretically and in connection to physical problems. On more speculative grounds, we argue that the origin of the applicability of the method stems from the non locality of the theory under consideration.