Local realizations of kinematical groups with a constant electromagnetic field. II. The nonrelativistic case

Abstract

In this paper, nonrelativistic elementary physical systems interacting with constant external electromagnetic fields are studied. The method is to construct a special kind of realizations of the Galilei group, which depend on the electromagnetic field. The linearization of this problem, which consists in obtaining these local realizations via the linear representations of another group, leads to a new representation group: the nonrelativistic Maxwell group. The study of the representations of this group and the related invariant equations completes this work.