For uniform systems of spinless fermions in d spatial dimensions with d > 1
, interacting through the isotropic two-body potential nu(r-r'), a celebrat
ed theorem due to Luttinger (1961) states that under the assumption of vali
dity of the many-body perturbation theory the self-energy Sigma(k ; epsilon
), with 0 less than or equal to k less than or similar to 3k(F) (where k(F)
stands for the Fermi wavenumber), satisfies the following universal asympt
otic relation as e approaches the Fermi energy epsilon(F) : Im [Sigma(k ; e
psilon)] similar to -/+alpha(k)(epsilon - epsilon(F))(2), epsilon greater t
han or less than epsilon(F) with alpha(k) greater than or equal to 0. As th
is is, by definition, specific to self-energies of the 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 necessari
ly break down. We demonstrate that Im [Sigma(k ; epsilon)] similar to -/+al
pha(k)(epsilon - epsilon(F))(2 epsilon) greater than or less than epsilon(F
), is implicit in Luttinger's proof and that, for d > 1, in principle nothi
ng prohibits a non-Fermi-liquid-type land, in particular a Luttinger-liquid
-type) Sigma(k ; epsilon) from being obtained within the framework of the m
any-body perturbation theory. We in addition indicate how seemingly innocuo
us 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 oth
erwise. Proofs that a certain metallic system is in a Fermi-liquid state, b
ased on such expansions, are therefore tautologies.