Effects of Lorentz invariance violation on particle acceleration and photon emission

In this study, we revisit the models of Fermi acceleration, incorporating Lorentz Invariance Violation (LIV) through a phenomenological approach. LIV is introduced via a modified Einstein's dispersion relation, along with an adjustment to the Lorentz factor. We calculate the energy spectrum and acceleration time of particles accelerated by first- and second-order Fermi mechanisms as a function of the energy at which LIV becomes significant. The second-order mechanism exhibited a shift in the spectral index, while the first-order model exhibited a significant suppression in the particle spectrum. Additionally, Synchrotron and Synchrotron Self-Compton (SSC) losses were incorporated into the first-order energy spectrum, with these processes also being modified by LIV. The effects on the spectra of charged particles were analyzed, as well as the resulting photon emissions from these losses. Synchrotron losses induced an energy barrier, while SSC led to a suppression in the number of particles. The LIV-modified SSC emission resulted in a new high-energy emission region, which is not observed in standard scenarios. This work advances the search for LIV in astroparticle physics by demonstrating, for the first time, how this hypothesis alters Fermi acceleration mechanisms, paving the way for a more comprehensive analysis in the future.