Exact factorization of the many-body Green's function theory of electrons and nuclei

TL;DR

This paper develops an exact Green's function approach for electrons and nuclei by integrating it with the wave function's exact factorization, extending beyond the Born-Oppenheimer approximation.

Contribution

It introduces a systematic, exact Green's function framework for electrons and nuclei that surpasses the limitations of the Born-Oppenheimer approximation.

Findings

Existing Born-Oppenheimer Green's functions are special cases of the new approach.

The body-fixed frame formulation is necessary for going beyond Born-Oppenheimer theory.

The lowest order electronic Green's function is an average over nuclear density.

Abstract

We combine the recently developed many-body Green's function theory for electrons and nuclei with the exact factorization of the wave function. The existing Born-Oppenheimer Green's functions are shown to be special cases of our exact approach. We consider the limitations of the laboratory frame formulation of the Green's function theory and discuss why the body-fixed frame formulation is needed in order to go beyond the Born-Oppenheimer theory. We give exact forms of the electronic and nuclear Green's functions written in terms of the exact factorized states, providing a systematic approach beyond the Born-Oppenheimer approximation. The lowest order approximation to the exact electronic Green's function is found to be an expected value of the Born-Oppenheimer electronic Green's function with respect to the nuclear density.