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Using many-body techniques we obtain the time-dependent Gaussianapproximation for interacting fermion-scalar field models. This method isapplied 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-calledquantum scalar plasma model. The renormalization for the resulting Gaussianmean-field equations, both static and dynamical, are examined and initialconditions discussed. We also investigate solutions for the gap equation andshow that the energy density has a single minimum.Comment: 21 pages, latex, 4 postscript figures, new sections, some literary  changes, notation corrections, accepted for publication in Phys. Rev

Fermion pairing dynamics in the relativistic scalar plasma