2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124719A scenario is presented on how to shift the predicted cutoff in the cosmic ray spectrum at 10**20 eV, called the Greisen-Zatsepin-Kuzmin limit (GKZ), to larger energies without breaking the Lorentz invariance. The formulation is based on a pseudo-complex extension of standard field theory. The dispersion relation of particles can be changed, leading to a modification of the GKZ limit. Maximal shifts are determined.4 pages, 1 figureHigh Energy Physics - Theorytext