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 $G_k\left(\zeta \right)$ 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, $\mathrm{Im} G_k(x-i{0}^{+})$ behaves like $C_k{(x-\mu )}^2$ ($C_k>0\mathrm{}$) for $x$ very near $\mu$, is proved.

• Received 1 October 1960

DOI:https://doi.org/10.1103/PhysRev.121.942