TL;DR
This paper introduces a pseudo-complex field theory with a minimal scalar length, leading to regularization, modified scattering cross sections, and potential shifts in cosmic ray spectrum limits.
Contribution
It presents a novel pseudo-complex formulation of field theory with an extended symmetry and minimal length, affecting scattering calculations and cosmic ray physics.
Findings
Calculated cross sections for electron scattering and Compton scattering.
Identified deviations due to the minimal scalar length.
Predicted a shift in the GZK limit of cosmic rays.
Abstract
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.
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