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.
Bibliographical noteFunding Information:
V.J.H. thanks Dr. Ivan Gonoskov for useful discussions on various aspects of the present work. E.K.U.G. acknowledges financial support by the European Research Council Advanced Grant FACT (ERC-2017-AdG-788890).
© 2020 authors. Published by the American Physical Society.