  We reproduce and review some of the main results of three of our earlier
papers, utilizing in doing so a considerably more transparent formalism than
originally utilized. The most fundamental result to which we pay especial
attention in this paper, is that the exact Fermi surface (FS) of the uniform
metallic ground state (GS) of any single-band Hamiltonian, describing fermions,
is a subset of the FS within the framework of the exact Hartree-Fock theory. We
also review some of the physical implications of the latter result. Our
considerations reveal that the interacting FS of a uniform metallic GS cannot
be calculated exactly to order \nu (\nu \ge 2) in the coupling constant \lambda
of the interaction potential in terms of the self-energy calculated to order
\nu in a non-self-consistent fashion. We show this to be interlinked with the
failure of the Luttinger-Ward identity, and thus of the Luttinger theorem, for
a self-energy that is not appropriately related to the single-particle Green
function from which the FS is deduced. We further show that the same mechanism
that embodies the Luttinger theorem within the framework of the exact theory,
accounts for a non-trivial dependence of the exact self-energy on \lambda that
cannot be captured within a non-self-consistent framework. We thus establish
that the extant calculations that purportedly prove deformation of the
interacting FS of the metallic GS of the single-band Hubbard Hamiltonian with
respect to its Hartree-Fock counterpart at the second order in the on-site
interaction energy U, are fundamentally deficient. In an appendix we show that
the number-density distribution function, to be distinguished from the
site-occupation distribution function, corresponding to the GS of the Hubbard
Hamiltonian is not non-interacting v-representable, a fact established earlier
numerically. [Abridged Abstract]
