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

TL;DR

This paper introduces a hyperfunction-based formulation of many-body Green's functions, offering a more elegant and natural description that could enhance theoretical tools in many-body physics.

Contribution

It presents a novel hyperfunction framework for single-particle Green's functions, clarifying their properties and relations within many-body theory.

Findings

Hyperfunctions provide an elegant description of Green's functions.

Standard results are recovered straightforwardly within this framework.

Potential for extending the formalism beyond single-particle functions.

Abstract

We show that the single-particle Green's functions used in many body theory have an elegant description in the form of hyperfunctions. We summarize the necessary hyperfunction concepts. We show that the analytical properties and the relations between different Green's functions are natural within this formulation. Important results from the standard formalism are recovered straightforwardly. We argue that hyperfunctions could possibly provide a powerful new tool for many body theory, if the formalism could be developed beyond single-particle Green's functions.