Gamma Ray Burst Constraints on Ultraviolet Lorentz Invariance Violation

We present a unified general formalism for ultraviolet Lorentz invariance violation (LV) testing through electromagnetic wave propagation, based on both dispersion and rotation measure data. This allows for a direct comparison of the efficacy of different data to constrain LV. As an example we study the signature of LV on the rotation of the polarization plane of $\gamma$-rays from gamma ray bursts in a LV model. Here $\gamma$-ray polarization data can provide a strong constraint on LV, 13 orders of magnitude more restrictive than a potential constraint from the rotation of the cosmic microwave background polarization proposed by Gamboa, L\'{o}pez-Sarri\'{o}n, and Polychronakos (2006).