  We present a formalism which enables us to express, for arbitrary d, the
behaviour of the momentum-distribution function n_{sigma}(k) pertaining to
uniform metallic ground states of the single-band Hubbard Hamiltonian H close
to S_{F;sigma} (the Fermi surface of the fermions with spin index sigma, sigma
= uparrow,downarrow) in terms of a small number of constant parameters which
are bound to satisfy certain inequalities implied by the requirement of the
stability of the ground state of the system. These inequalities restrict the
range of variation of n_{sigma}(k) for k infinitesimally inside and outside the
Fermi sea pertaining to fermions with spin index sigma and consequently the
range of variation of the zero-temperature limit of n_{sigma}(k) for k on
S_{F;sigma}. On the basis of some available accurate numerical results for
n_{sigma}(k) pertaining to the Hubbard and the t-J Hamiltonian, we conclude
that, at least in the strong-coupling regime, the metallic ground states of H
for d=2 cannot be Fermi-liquid, nor can they in general be purely Luttinger- or
marginal-Fermi liquids. We further rigorously identify the pseudo-gap
phenomenon, or `truncation' of the Fermi surface, clearly observed in the
normal states of under-doped copper-oxide superconductors, as corresponding to
a line of resonance energies located below the Fermi energy, with a concomitant
suppression to zero of the jump in n_{sigma}(k) over the `truncated' parts of
the Fermi surface. [Short Abstract]
