High energy constraints on Lorentz symmetry violations

Lorentz violation at high energies might lead to non linear dispersion relations for the fundamental particles. We analyze observational constraints on these without assuming any a priori equality between the coefficients determining the amount of Lorentz violation for different particle species. We focus on constraints from three high energy processes involving photons and electrons: photon decay, photo-production of electron-positron pairs, and vacuum Cerenkov radiation. We find that cubic momentum terms in the dispersion relations are strongly constrained.