Stable and resonant Cooper pairs

A Bethe-Salpeter treatment of Cooper pairs (CPs) based on an ideal Fermi gas (IFG) ‘sea’ yields the familiar stable negative-energy, infinite-lifetime two-particle bound-state if two-hole CPs are ignored. Otherwise, it gives purely imaginary energies and thus unphysical solutions. However, a Bogoliubov transformation to the BCS ground state yields the trivial sound solution plus a nontrivial one. The latter are two-fermion ‘moving CPs’ as positive-energy stable objects for zero center-of-mass momentum (CMM), and finite-lifetime resonant ones for nonzero CMM with a linear dispersion leading term. Hence, Bose-Einstein condensation of such pairs may occur in exactly two dimensions as it cannot with quadratic dispersion.