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 Gₖ(ζ) 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 Gₖ(x-i0⁺) behaves like Cₖ(x-μ)² (Cₖ>0) for x very near μ, is proved.
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J. M. Luttinger (1961) studied this question.
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