Theory of resonant Raman scattering: Towards a comprehensive ab initio description

We develop a general, fully quantum mechanical theory of Raman scattering from first principles in terms of many-body correlation functions. In order to arrive at expressions that are practically useful in the context of condensed matter physics, we adopt the Lehmann-Symanzik-Zimmermann reduction formula from high-energy physics and formulate it in the language of many-body perturbation theory. This enables us to derive a general and practically useful expression for the Raman scattering rate in terms of quantities that can be computed ab initio. Our work paves the way toward a comprehensive computational approach to the calculation of Raman spectra that goes beyond the current state of the art by capturing both excitonic and nonadiabatic effects.