Nonequilibrium dynamics of fermions in a spatially homogeneous scalar background field

TL;DR

The paper develops a covariant, nonequilibrium quantum-field-theory framework for a spatially homogeneous scalar field $\phi(t)$ coupled to fermions via a Yukawa interaction, incorporating one-loop back-reaction and a renormalization scheme suitable for numerical computation. Initial Stueckelberg-type singularities are removed with a Bogoliubov transformation, and the formalism is extended to a spatially flat FRW spacetime, with conformal-time rescaling ensuring renormalization parallels Minkowski space. Numerical Minkowski-space simulations reveal that fermionic fluctuations can be dynamically significant and do not always act as a mere damping channel; in some regimes they generate resonance-like particle production bands and can even catalyze the growth of bosonic fluctuations. The results challenge the assumption of fermions being universally inefficient for dissipation and suggest complex interplay between fermionic back-reaction and scalar/quasilinear dynamics that may be relevant for cosmology and nonequilibrium quantum fields. Overall, the work provides a robust framework for studying nonequilibrium fermion dynamics in strong-field backgrounds and lays groundwork for analytical follow-up using, e.g., Mathieu-type analyses.

Abstract

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 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 assumed previously 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.