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In the [BCS] paper the theory of superconductivity was developed for the BCSmodel, in which the (instantaneous) interaction is only between fermions ofopposite momentum and spin. Such model was analyzed by variational methods,finding that a superconducting behavior is energetically favorable.Subsequently it was claimed that in the thermodynamic limit the BCS model isequivalent to the (exactly solvable) quadratic mean field BCS model; a rigorousproof of this claim is however still lacking. In this paper we consider the BCSmodel with a finite range temporal interaction, and we prove rigorously itsequivalence with the mean field BCS model in the thermodinamic limit if therange is long enough, by a (uniformly convergent) perturbation expansion aboutmean field theory.Comment: 14 page

Mass Generation in a Fermionic Model with Finite Range Time Dependent Interactions