On the (anisotropic) uniform metallic ground states of fermions interacting through arbitrary two-body potentials in d dimensions

We demonstrate that the skeleton of the Fermi surface S_{F;s} pertaining to a uniform metallic ground state (corresponding to fermions with spin index s) is determined by the Hartree-Fock contribution to the dynamic self-energy. The Fermi surface S_{F;s} consists of all points which in addition to satisfying the quasi-particle equation in terms of the Hartree-Fock self-energy, fulfill the equation S_{s}(k) = 0, where S_{s}(k) is defined in the main text; the set of k points which satisfy the Hartree-Fock quasi-particle equation but fail to satisfy S_{s}(k) = 0, constitute the pseudo-gap region of the putative Fermi surface of the interacting system. We consider the behaviour of the ground-state momentum-distribution function n_{s}(k) for k in the vicinity of S_{F;s} and show that whereas for the uniform metallic ground states of the conventional Hubbard Hamiltonian n_{s}(k) is greater/less than 0.5 for k approaching S_{F;s} from inside/outside the Fermi sea, for interactions of non-zero range these inequalities can be violated (without thereby contravening the condition of the non-negativity of the possible jump in n_{s}(k) on k crossing S_{F;s} from directly inside to directly outside the Fermi sea). We discuss, in the light of the findings of the present work, the growing experimental evidence with regard to the `frustration' of the kinetic energy of the charge carriers in the normal states of the copper-oxide-based high-temperature superconducting compounds. [Short abstract]