We perform real-time numerical lattice simulations of a one-family version of the Standard Model. We model the quantum fermions using the ensemble method and treat the bosonic scalar and non-abelian gauge fields classically. Our main interest is electroweak baryogenesis, and we test the approach by considering Standard Model baryon number violation through the chiral anomaly, a truly quantum phenomenon. We find that the method correctly reproduces the anomaly, and perform the first dynamical simulations of electroweak baryon number violation including fermions.
Saffin, P. M., & Tranberg, A. (2012). Dynamical simulations of electroweak baryogenesis with fermions. Journal of High Energy Physics, 2012(2), https://doi.org/10.1007/JHEP02%282012%29102