Fermion Pairing Dynamics in the Relativistic Scalar Plasma

TL;DR

This paper develops a time-dependent Gaussian approximation for relativistic fermion-scalar field models, analyzing the dynamics of fermion pairing and energy density in a quantum scalar plasma.

Contribution

It introduces a novel time-dependent Gaussian approach to study fermion pairing dynamics in relativistic scalar plasma models, including renormalization and gap equation solutions.

Findings

Energy density exhibits a single minimum.

Renormalized static and dynamical mean-field equations are derived.

Solutions to the gap equation are analyzed.

Abstract

Using many-body techniques we obtain the time-dependent Gaussian approximation for interacting fermion-scalar field models. This method is applied to an uniform system of relativistic spin-1/2 fermion field coupled, through a Yukawa term, to a scalar field in 3+1 dimensions, the so-called quantum scalar plasma model. The renormalization for the resulting Gaussian mean-field equations, both static and dynamical, are examined and initial conditions discussed. We also investigate solutions for the gap equation and show that the energy density has a single minimum.