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

The method of many body Green's functions is used to describe an arbitrary system of electrons and nuclei in a rigorous manner given the Hamiltonian of Coulombic interactions and kinetic energies. The theory given resolves the problem arising from the translational and rotational invariance of the Hamiltonian afflicting the existing theory based on the same technique. As a result, we derive a coupled set of exact equations for the electron and nuclei Green's functions giving a systematic way to potentially compute various properties of a rather arbitrary many-body systems of electrons and nuclei beyond Born-Oppenheimer approximation, including molecules and solids. We discuss a special case of crystalline solids in more detail.