Non-local dielectric functions in classical electrostatics and QCD models

In order to resolve the problem of infinite forces and renormalizability of the self-energy of point charges in non-uniform local dielectric media, we propose a formalism based on a non-local dielectric function. Implications for both solid-state physics and chromodielectric models of QCD are discussed. The formalism to calculate the energies of systems of charges is developed. The (integral) equation for the Green function is explicitly solved both for a slowly varying dielectric medium and for the planar boundary, and the results are compared with those of the local approach. (Author)