Interaction of Charged Particles in a Dielectric

This paper is a sequel to an earlier study, from a many-particle standpoint, of the motion of an electron (or hole) in an insulator. We consider an insulator (whose nuclei are taken as fixed), including the electron-electron interaction. It is then shown that the static dielectric constant defined in terms of the force between two distant point charges immersed in the medium, and the effective dielectric constant ^*, which determines the force between an extra electron (or hole) and a distant point charge, are equal. These results may be summarized by the statement that, if sufficiently distant, external charges in a dielectric interact with each other and with the charge of an extra electron or hole as if all charges were renormalized according to the prescription Q{^1{2}}. The method of proof is to treat the Coulomb interactions between the electrons and between the electrons and external charges by perturbation theory and to establish a correspondence, to all orders, between the Feynman graphs which define and those which define ^*. The result is therefore exact, at least as long as the perturbation series converge.