2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57156We show that the particle number density derived from the thermodynamic Green's function at temperature zero constructed in the second part of this series has a jump across the Fermi curve, a basic property of a Fermi liquid. We further show that the two particle thermodynamic Green's function at temperature zero has the regularity behavior expected in a Fermi liquid.73 pages, 3 figuresMathematical Physics82B28 (Primary) 81T08 (Secondary)text