Sum rules for the optical constants

A number of sum rules for the optical constants, in particular, the refractive index of a nonconducting medium, are obtained. Some of the sum rule constraints are highly damped for large frequencies, exponentially in one particular case. Formal integral relationships for the index of refraction at complex frequencies are presented. Sum rules based on known experimental points for which n (ω)−1 has zeros are indicated. An outline of a modified derivation of some recently presented sum rules for the optical constants is given.