Fermi Acceleration Mechanisms Beyond Lorentz Symmetry

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 $κ$-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.

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