Covariance group in the presence of external electromagnetic fields

In the frame of a research program concerned with the investigation by group theoretical methods of space-time symmetries of interacting systems the author explicitly derives in this paper the general covariance group for a charged particle moving in an arbitrary external (classical) electromagnetic field. This group is obtained independently of any equation of motion, essentially on the simple basis of the invariance properties of the Maxwell equations under Poincare transformations. As a consequence of these results, the group theoretical definition of an elementary particle can usefully be extended to the case where an external field is present, and useful information can be obtained on the characterization of covariant equations of motion. (Auth.)