The sense in which the f-sum rule is satisfied is discussed.
The f-sum rule may also be regarded as a high-frequency limit of the Kramers-Kronig relations (5); in this case, the multiplication by [omega] before Eq.
The f-sum rule should apply to all response functions that satisfy Eq.
13), it is possible to form the f-sum rule integral of Eq.
This example turns out to be the only relation that is not widely discussed which is needed to complete the discussion of the f-sum rule for Lindhard's transverse dielectric function.
The tradition point of view is that the f-sum rule fails and the formula must be rewritten to include a pole term explicitly.
The key requirements for the f-sum rule are causality, which implies there are no poles in the upper-half complex frequency plane, and the free-electron response at high frequencies.