A mathematical analysis of the GW ^o method for computing electronic excited energies of molecules

This article is concerned with the GW method for finite electronic systems. In the first step, we provide a mathematical framework for the usual one-body operators that appear naturally in many-body perturbation theory. We then give a rigorous mathematical formulation of the GW0 equations, and study the well-posedness of these equations, proving the existence of a unique solution in a perturbative regime.