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A class of sum rules for inelastic light scattering is developed. We showthat the first moment of the non-resonant response provides information aboutthe potential energy in strongly correlated systems. The polarizationdependence of the sum rules provide information about the electronicexcitations in different regions of the Brillouin zone. We determine the sumrule for the Falicov-Kimball model, which possesses a metal-insulatortransition, and compare our results to the light scattering experiments inSmB_6.Comment: (5 pages, 3 figures, typeset in ReVTeX

Optical Sum Rules that Relate to the Potential Energy of Strongly Correlated Systems