Superconvergence and Sum Rules for the Optical Constants

A systematic procedure is given for the derivation of sum rules for the optical constants of material media from dispersion relations, in analogy with superconvergence techniques of high-energy physics. In addition to the well-known $f$-sum rules, a number of new sum rules are obtained for the refractive index, the dielectric tensor, and its inverse. In particular, it is shown that the average value of the real refractive index over the whole frequency spectrum is equal to unity. The physical implications of the new results are discussed in connection with the dispersion of optical constants, with the effect of external perturbations, and with the theory of natural optical activity.