Fermion Pairing Dynamics in the Relativistic Scalar Plasma

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.