On the statistical mechanics of matter in an electromagnetic field. I. Derivation of the maxwell equations from electron theory

Abstract

Maxwell's macroscopic field equations are derived from the fundamental microscopic equations of electron theory in a new way. Instead of the usual space-time averaging procedure a statistical ensemble averaging method is applied, which is perhaps more satisfactory both from a physical and from a mathematical point of view. The treatment is valid for multicomponent systems, in which every component may move in an arbitrary way, so that e.g. diffusion phenomena are included. Furthermore it would seem that the method given here is also suitable for the discussion of other problems connected with the behaviour of matter in an electromagnetic field