Fermion effective dispersion relation for z=2 Lifshitz QED

We study consequences of Lorentz symmetry violation in a z=2 Lifshitz extension of QED in 3+1 dimensions, and we discuss non-trivial effects of quantization. Because of the specific power of space momentum in propagators of the model, dimensional regularization leads to an unusual interpretation of loop integrals, which are finite even when the space dimension goes to the integer 3. We check the consistency of the approach by calculating the (vanishing) corrections to the photon mass and the IR-divergence-free corrections to the dispersion relation for massless fermions.