Pairing between two fermionic excitations in a non-Fermi liquid is considered in terms of the Bethe-Salpeter equation. We consider the pairing in a Fermi system with vanishing spectral weight. It is well known that the quasiparticle pole in the single-particle Green's function in a Non-Fermi liquid is absent or weak. The examples of such systems can be viewed as the "Marginal" Fermi liquid and Luttinger liquid. Another example that has also been considered is the Fermi system with pseudogap behavior in the spectral weight. Although the pairing between two excitations in a non-Fermi liquid is, in general, absent, nevertheless we show that the Cooper's type of pairing can occur and the conditions for such a kind of pairing are discussed. The results have also been applied to the systems with smeared or non-monotonic Fermi distribution. A system that transits from Fermi-type to Bose-type behavior can serve as an example of such systems as discussed.
We study in this paper the general properties of a many body system of fermions in arbitrary dimensions assuming that the {\em momentum} of individual fermions are good quantum numbers of the system. We call these systems
k-Fermi liquids. We show how Fermi liquid, Luttinger liquid (or Fermi liquid with exclusion statistics) and spin-charge separation arises from this framework. Two exactly solvable
k-Fermi liquid models with spin-charge separation are discussed as examples.