New constraints on Planck-scale lorentz violation in QED from the crab nebula

We set constraints on O(E/M) Lorentz violation in QED in an effective field theory framework. A major consequence of such assumptions is the modi. cation of the dispersion relations for electrons/positrons and photons, which in turn can affect the electromagnetic output of astrophysical objects. We compare the information provided by multiwavelength observations with a full and self-consistent computation of the broad-band spectrum of the Crab Nebula. We cast constraints of the order of 10(-5) at 95% confidence level on the lepton Lorentz violation parameters.