One-loop renormalization of Lorentz-violating electrodynamics

We show that the general Lorentz- and CPT-violating extension of quantum electrodynamics is one-loop renormalizable. The one-loop Lorentz-violating beta functions are obtained, and the running of the coefficients for Lorentz and $\mathrm{CPT}$ violation is determined. Some implications for theory and experiment are discussed.