On Sum Rules for Scattering in Circular Polarization

Classical sum rules, that connect the dynamic scattering properties at all frequencies to the static polarizability, can be shown to break down when applied to circular polarization. This has previously been explained in terms of a breach of symmetry with respect to positive and negative frequencies. In this paper, we show an alternative explanation where circular polarization is introduced by using a branch cut in the complex plane. A numerical example for a spherical helical scatterer illustrates the results.