Rotation and Lorentz Groups in a Finite Geometry

Abstract
The introduction in physics of a finite geometry approximating the ordinary Euclidean one poses the problem of studying the relativity groups over such a geometry. We present a detailed analysis of the structure and irreducible representations of the rotation, Lorentz, and Poincaré groups. It is found that, besides the usual quantum numbers, a new two-valued label is necessary to specify the representations.