Fermi Acceleration Mechanisms Beyond Lorentz Symmetry
arXiv:2601.04961
The authors construct models of first- and second-order Fermi acceleration that include generic frame transformations, dispersion relations, and conservation laws, and study how deformations or violations of Lorentz symmetry using the κ‑Poincaré algebra affect particle energy spectra. They compare the predicted spectra with Pierre Auger cosmic‑ray data.
Abstract
We construct models for first- and second-order Fermi acceleration of particles, incorporating generic frame transformations, dispersion relations, and conservation laws. Within this framework, we study deformations of Lorentz symmetry via the -Poincaré algebra in the bicrossproduct and classical bases, which respectively deform and preserve the relativistic dispersion relation. We also examine explicit Lorentz symmetry violation and compare the results with deformed relativity and special relativity. The energy spectra present different shapes when one considers deformation or violation of Lorentz symmetry in superluminal or subluminal scenarios. One of the possible outcomes is an intense decay of the spectrum for higher energies. We compare our results with Pierre Auger data.
23 pages. Added a section with comparison with data