**Authors**:
Vieri Mastropietro

**Title** *
Gap generation in the BCS model
with finite range time dependent
interaction
*

**Abstract:**
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 time dependent
interaction, and we
prove rigorously its equivalence with the mean field BCS model
in the thermodynamic limit
if the range is long enough,
by a (uniformly convergent) perturbation expansion about mean field theory.

**Key words: ** BCS model, Superconductivity

Vieri Mastropietro

Matematica, Universita' di Roma 2

V.le
della Ricerca Scientifica

00133 Roma, Italia

tel +39-06-7259-4209

em: mastropi@mat.uniroma2.it

http://ipparco.roma1.infn.it