Landau-Fermi liquids without quasiparticles

Landau-Fermi liquid theory is conventionally believed to hold whenever the interacting single-particle density of states develops a $\delta$-like component at the Fermi surface, which is associated with quasiparticles. Here we show that a microscopic justification can be actually achieved under more general circumstances, even in case coherent quasiparticles are totally missing and the interacting single-particle density of states vanishes at the chemical potential as consequence of a pole singularity in the self-energy.