  A Lorentz violating modification of massless QED is proposed, with higher
order space derivatives for the photon field. The fermion dynamical mass
generation is studied with the Schwinger-Dyson approach. Perturbative
properties of the model are calculated at one-loop and discussed at
higher-order loops, showing the consistency of the model. We explain that there
is no contradiction with the definition of the speed of light c, although
fermions see an an effective light cone, with a maximum speed smaller than c.
