  For uniform systems of spin-less fermions in d spatial dimensions with d > 1,
interacting through the isotropic two-body potential v(r-r'), a celebrated
theorem due to Luttinger (1961) states that under the_assumption_ of validity
of the many-body perturbation theory the self-energy Sigma(k;epsilon), with 0
<,= k <,~ 3 k_F (where k_F stands for the Fermi wavenumber), satisfies the
following universal asymptotic relation as epsilon approaches the Fermi energy
epsilon_F: Im[Sigma(k;epsilon)] ~ -,+ alpha_k (epsilon-epsilon_F)^2, epsilon
>,< epsilon_F, with alpha_k >,= 0. As this is, by definition, specific to
self-energies of Landau Fermi-liquid systems, treatment of non-Fermi-liquid
systems are therefore thought to lie outside the domain of applicability of the
many-body perturbation theory; that, for these systems, the many-body
perturbation theory should_necessarily_ break down. We demonstrate that
Im[Sigma(k;epsilon)] ~ -,+ alpha_k (epsilon-epsilon_F)^2, epsilon >,<
epsilon_F, is_implicit_ in Luttinger's proof and that, for d > 1, in principle
nothing prohibits a non-Fermi-liquid-type (and, in particular
Luttinger-liquid-type) Sigma(k;epsilon) from being obtained within the
framework of the many-body perturbation theory. We in addition indicate how
seemingly innocuous Taylor expansions of the self-energy with respect to k,
epsilon or both amount to tacitly assuming that the metallic system under
consideration is a Fermi liquid, whether the self-energy is calculated
perturbatively or otherwise. Proofs that a certain metallic system is in a
Fermi-liquid state, based on such expansions, are therefore tautologies.
