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We show that the single-particle Green's functions used in many body theoryhave an elegant description in the form of hyperfunctions. We summarize thenecessary hyperfunction concepts. We show that the analytical properties andthe relations between different Green's functions are natural within thisformulation. Important results from the standard formalism are recoveredstraightforwardly. We argue that hyperfunctions could possibly provide apowerful new tool for many body theory, if the formalism could be developedbeyond single-particle Green's functions.

Hyperfunction formulation of many body Green's functions and the Matsubara formalism