A New Limit on Planck Scale Lorentz Violation from Gamma-ray Burst
  Polarization
  Constraints on possible Lorentz invariance violation (LIV) to first order in
$E/M_{\rm Planck}$ for photons in the framework of effective field theory (EFT)
are discussed, taking cosmological factors into account. Then, using the
reported detection of polarized soft $\gamma$-ray emission from the
$\gamma$-ray burst GRB041219a that is indicative of an absence of vacuum
birefringence, together with a very recent improved method for estimating the
redshift of the burst, we derive constraints on the dimension 5 Lorentz
violating modification to the Lagrangian of an effective local QFT for QED. Our
new constraints are more than five orders of magnitude better than recent
constraints from observations of the Crab Nebula. We obtain the upper limit on
the Lorentz violating dimension 5 EFT parameter $|\xi|$ of $2.4 \times
10^{-15}$, corresponding to a constraint on the dimension 5 standard model
extension parameter, $k^{(5)}_{(V)00} \le 4.2 \times 10^{-34}$ GeV$^{-1}$.
