Real time dynamics with fermions on a lattice

The 1+1 dimensional abelian Higgs model with fermions is a toy model for
the theory of electroweak baryogenesis. We study the dynamics of the model
with axially coupled fermions in real-time. The model is defined on a
spacetime lattice to preserve gauge invariance and to obtain numerical
stability in a simple way. We take into account the phenomenon of lattice
fermion doubling. The dynamics is approximated by treating the inhomogeneous
Bose fields classically, which is justified in a large N_f approximation.
The back reaction on the Bose fields due to fermion field fluctuations is
calculated using a mode function expansion. We discuss and present numerical
results for the response of fermions to sphaleron transitions, the
renormalizability of the effective equations of motion and non-perturbative
dynamics in the framework of non-equilibrium quantum field theory. The
long-time behaviour of the system is discussed and we speculate about
applications to finite density calculations.