Mass generation in a fermionic model with finite range time dependent interactions

Bardeen, Cooper and Schrieffer in their paper on the theory of superconductivity introduced a model of interacting fermions (BCS model) in which the (instantaneous) interaction is only between electrons of opposite momentum and spin (Cooper pairs). Subsequently it was claimed that in the thermodynamic limit the BCS model is equivalent to the (exactly solvable) quadratic mean field BCS model in which the phenomenon of mass generation is present; a rigorous proof of this equivalence is however still an open problem. In this paper we consider an interacting fermionic model in which the Cooper pairs interact through a finite range time dependent interaction. For this model (quartic in the fermions and not solvable) we are able to prove the generation of mass in the thermodynamic limit and its equivalence with the mean field BCS model. The proof is achieved by a convergent perturbation expansion about mean field theory.