2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/193154We set constraints on O(E/M) Lorentz Violation in QED in an effective field theory framework. A major consequence of such assumptions is the modification 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 order 10^{-5} at 95% confidence level on the lepton Lorentz Violation parameters.23 pages, 9 figures. v2: added comments and references, matches version accepted by JCAPAstrophysicsGeneral Relativity and Quantum CosmologyHigh Energy Physics - PhenomenologyHigh Energy Physics - Theorytext