A new way to deal with fermions in Monte Carlo simulations

Abstract

An exact, nonlocal, finite step-size algorithm for Monte Carlo simulation of theories with dynamical fermions is proposed. The algorithm is based on obtaining the new configuration U' from the old one U by solving the equation $ M(U') η= ωM(U) η$, where $M$ is fermionic operator, $η$ is random Gaussian vector, and $ω$ is random real number close to unity. This algorithm can be used for the acceleration of current simulations in theories with Grassmann variables. A first test was done for SU(3) QCD with purely fermionic term in the action.