  In the [BCS] paper the theory of superconductivity was developed for the BCS
model, in which the (instantaneous) interaction is only between fermions of
opposite 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 is
equivalent to the (exactly solvable) quadratic mean field BCS model; a rigorous
proof of this claim is however still lacking. In this paper we consider the BCS
model with a finite range temporal interaction, and we prove rigorously its
equivalence with the mean field BCS model in the thermodinamic limit if the
range is long enough, by a (uniformly convergent) perturbation expansion about
mean field theory.
