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Much attention has been given to a possible violation of the optical sum rulein the cuprates, and the connection this might have to kinetic energy lowering.The optical integral is composed of a cut-off independent term (whosetemperature dependence is a measure of the sum rule violation), plus a cut-offdependent term that accounts for the extension of the Drude peak beyond theupper bound of the integral. We find that the temperature dependence of theoptical integral in the normal state of the cuprates can be accounted forsolely by the latter term, implying that the dominant contribution to theobserved sum rule `violation' in the normal state is due to the finite cut-off.This cut-off dependent term is well modeled by a theory of electronsinteracting with a broad spectrum of bosons.

Optical Integral in the Cuprates and the Question of Sum Rule Violation