A new way to deal with fermions in Monte Carlo simulations

An exact, nonlocal algorithm for Monte Carlo simulation of theories with dynamical fermions is proposed. The algorithm is based on obtaining the new configuration Ũ from the old one U by solving the equation M(Ũ)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 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.