Some extensions and applications of dispersion relations

摘要

The rationale of dispersion relations (DR) is traced to von Neumann's "state properties" and is given a unifying formulation by the introduction of "equations of restriction". Some questions surrounding reciprocal relations in the time domain are discussed. Then, extensions of DR to multi-variable cases are formulated through extended "equations of restrictions", which may be exact or approximate. These equations are applied to nonlocal dielectrics (admitting of polariton modes), which are shown to obey (in general) light-cone causality, though cases might occur in which a modification of the postulated dielectric functions is needed. [References: 23]