The classical electrodynamics of $N$ charged pointlike particles, moving in the space-time of two dimensions, is studied. The exact solution of this model is found, and its properties connected with the Poincaré group in two dimensions are described. In the case of $N=2\mathrm{}$, our solution reduces to a model of relativistic classical mechanics discovered by Currie and Jordan and by Beard and Fong. Nonlinear generalizations of the model are also discussed.

• Received 15 June 1970

DOI:https://doi.org/10.1103/PhysRevD.3.864