Nonequilibrium dynamics of fermions in a spatially homogeneous scalar background field

We consider the time evolution of systems in which a spatially homogeneous scalar field is coupled to fermions. The quantum back reaction is taken into account in the one-loop approximation. We set up the basic equations and their renormalization in a form suitable for numerical computations. The initial singularities appearing in the renormalized equations are removed by a Bogoliubov transformation. The equations are then generalized to those in a spatially flat Friedmann-Robertson-Walker universe. We have implemented the Minkowski space equations numerically and present results for the time evolution with various parameter sets. We find that fermion fluctuations are not in general as ineffective as previously assumed, but show interesting features which should be studied further. In an especially interesting example we find that fermionic fluctuations can “catalyze” the evolution of bosonic fluctuations.