  A new formulation of field theory is presented, based on a pseudo-complex
description. An extended group structure is introduced, implying a minimal
scalar length, rendering the theory regularized a la Pauli-Villars. Cross
sections are calculated for the scattering of an electron at an external
Coulomb field and the Compton scattering. Deviations due to a smallest scalar
length are determined. The theory also permits a modification of the minimal
coupling scheme, resulting in a generalized dispersion relation. A shift of the
Greisen-Zatsepin-Kuzmin-limit (GZK) of the cosmic ray spectrum is the
consequence.
