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

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₊ () 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, Im G₊ (x-i0^+) behaves like C₊ (x-) ^2 (C₊>0) for x very near, is proved.