A Bethe-Salpeter treatment of Cooper pairs (CPs) based on an ideal Fermi gas (IFG) "sea"' yields the familiar negative-energy, two-particle bound-state if two-hole CPs are ignored, but is meaningless otherwise as it gives purely-imaginary energies. However, when based on the BCS ground state, legitimate two-particle "moving" CPs emerge but as positive-energy, finite-lifetime resonances for nonzero center-of-mass momentum, with a \textit{linear}dispersion leading term. Bose-Einstein condensation of such pairs may thus occur in exactly two dimensions as it cannot with quadratic dispersion.
@article{arxiv.cond-mat/0306726,
title = {Generalized Cooper pairing and Bose-Einstein condensation},
author = {V. C. Aguilera-Navarro and M. Fortes and M. de Llano},
journal= {arXiv preprint arXiv:cond-mat/0306726},
year = {2007}
}