Optical sum rules that relate to the potential energy of strongly correlated systems

A class of sum rules for inelastic light scattering is developed. We show that the first moment of the non-resonant response provides information about the potential energy in strongly correlated systems. The polarization dependence of the sum rules provide information about the electronic excitations in different regions of the Brillouin zone. We determine the sum rule for the Falicov-Kimball model, which possesses a metal-insulator transition, and compare our results to the light scattering experiments in SmB_6.