Fermi Acceleration Mechanisms Beyond Lorentz Symmetry

TL;DR

This paper develops models for particle acceleration mechanisms considering Lorentz symmetry deformations, analyzing their effects on relativistic dispersion relations and comparing different symmetry frameworks.

Contribution

It introduces models for Fermi acceleration incorporating Lorentz symmetry deformations, including $$-Poincare9 algebra and explicit Lorentz violation, expanding understanding of particle acceleration in modified relativistic contexts.

Findings

Deformations of Lorentz symmetry affect particle acceleration processes.

Comparison between deformed relativity and special relativity reveals distinct effects.

Models show how Lorentz symmetry modifications influence particle energy spectra.

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 $\kappa$-Poincar\'e 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.