New Limits on Planck Scale Lorentz Violation in QED

Constraints on possible Lorentz symmetry violation (LV) of order $E/M_{\mathrm{P}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{k}}$ for electrons and photons in the framework of effective field theory (EFT) are discussed. Using (i) the report of polarized MeV emission from GRB021206 and (ii) the absence of vacuum Čerenkov radiation from synchrotron electrons in the Crab Nebula, we improve previous bounds by ${10}^{-10}$ and ${10}^{-2}$, respectively. We also show that the LV parameters for positrons and electrons are different, discuss electron helicity decay, and investigate how prior constraints are modified by the relations between LV parameters implied by EFT.