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A Lorentz violating modification of massless QED is proposed, with higherorder space derivatives for the photon field. The fermion dynamical massgeneration is studied with the Schwinger-Dyson approach, and it is found thatthe resulting mass is many orders of magnitude smaller than the (Plank-) massscale introduced by the higher order derivative terms. This is due to asuppressing factor, non-analytic in the fine structure constant andexponentially small. This scenario is an alternative to the Higgs mechanism forthe electron mass, which arises here from Lorentz violating effects at highenergies.

Dynamical mass generation in Lorentz-violating QED