Quasirelativistische Urfermionen

In recent papers we have reformulated the quantum theory of fermions in a lattice space with a finite number of points, sayZ ³. Of course, Lorentz invariance holds only in the limitZ→∞. So far a lattice space withZ ³ points provides us only with a convenient method to define the order of some limiting processes. — Here we discuss a more fundamental question. According to general relativity Lorentz invariance can not hold all over the world and must also be broken at tiny distances of the centers of particles. If the space curvature is not essential for the theory of elementary particles, as generally is assumed, we must only take into account the topological structure of the deviations from Lorentz invariance. In this respect the lattice space provides us with a rather rough but sufficient picture of a space, being approximately Lorentz invariant only for intermediate distances. — In a lattice withZ ³ points the Hilbert space has a finite number of dimensions. It seems to us important that this assumption will hold, even if we proceed to a more refined space model.