# Many-body Green's function theory of electrons and nuclei beyond the Born-Oppenheimer approximation

## TL;DR

This paper develops a comprehensive many-body Green's function framework for electrons and nuclei that goes beyond the Born-Oppenheimer approximation, addressing invariance issues and enabling systematic property calculations.

## Contribution

It introduces a coupled set of exact equations for electronic and nuclear Green's functions applicable to arbitrary systems beyond the Born-Oppenheimer approximation.

## Key findings

- Addresses translational and rotational invariance problems.
- Provides systematic approximation methods.
- Applicable to crystalline solids.

## Abstract

The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here resolves the problems arising from the translational and rotational invariance of this Hamiltonian that afflict the existing many-body Green's function theories. We derive a coupled set of exact equations for the electronic and nuclear Green's functions and provide a systematic way to approximately compute the properties of arbitrary many-body systems of electrons and nuclei beyond the Born-Oppenheimer approximation. The case of crystalline solids is discussed in detail.