Some consequences of the Luttinger theorem: The Luttinger surfaces in non-Fermi liquids and Mott insulators

Landau and Luttinger have shown that the properties of so-called Fermi liquids are determined by the Fermi surface of their excitations. The present analysis of mathematics of the Luttinger paper proves that non-Fermi liquids where there are no well-defined excitations and Mott insulators are essentially characterized by the Fermi-surface analog---the Luttinger surface, a feature of particle's propagator.