Elementary Particles in a Finite World Geometry

To account for the elementary particles a new physical geometry may be needed. A previous suggestion that this geometry may be finite is followed up by determining the representations of the orthogonal (Lorentzlike) group. Because of the existence of a new type of orthogonality-preserving transformation some of the representations are multiple-valued. A change of value is identified with a gauge transformation and electric charge is recognized as a certain number determining the many-valuedness of the representation. This charge number reverses sign under space inversion. The charged pions and sigma particles are correlated with some of the new representations.