Analytic Properties of Single-Particle Propagators for Many-Fermion Systems

Abstract

Certain general properties of single-particle propagators for a system of interacting fermions are derived. In addition, the properties of the proper self-energy part ${G}_{k}(\ensuremath{\zeta})$ which were used in previous work on the ground-state energy and on the Fermi surface are established. In particular, the fact that to all orders of perturbation theory in the interaction, $\mathrm{Im} {G}_{k}(x\ensuremath{-}i{0}^{+})$ behaves like ${C}_{k}{(x\ensuremath{-}\ensuremath{\mu})}^{2}$ (${C}_{k}>0$) for $x$ very near $\ensuremath{\mu}$, is proved.