The Total Green's Function of a Non-Interacting System

TL;DR

This paper computes the total Green's function for a non-interacting many-body system's time-dependent Schrödinger equation, providing a new perspective that could reshape understanding in perturbative many-body physics.

Contribution

It presents the first explicit calculation of the total Green's function for a non-interacting system, filling a longstanding gap in many-body theory literature.

Findings

Total Green's function derived for non-interacting systems

Provides a new framework for interpreting perturbative many-body physics

Lays groundwork for future studies on interacting systems

Abstract

Despite its centrality in the mathematical structure of perturbative many-body theory, the total Green's function for the many-body time-dependent Schrodinger equation has been ignored for decades, superseded by single-particle Green's functions, for which a vast portion of the literature has been devoted. In this paper, we give the first computation the total Green's function for the time-dependent Schrodinger equation for a non-interacting system of identical particles, setting the stage for a fresh interpretation of perturbative many-body physics.