Beyond Fermi-Liquid Theory: the $k$-Fermi liquids

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.