Low-cost fermions in classical field simulations

We discuss the possible extension of the bosonic classical field theory simulations to include fermions. This problem has been addressed in terms of the inhomogeneous mean-field approximation by Aarts and Smit. By performing a stochastic integration of an equivalent set of equations we can extend the original 1+1 dimensional calculations so that they become feasible in higher dimensions. We test the scheme in 2+1 dimensions and discuss some classical applications with fermions for the first time, such as the decay of oscillons