  We first comment on the search for a deviation from the linear photon
dispersion relation, in particular based on cosmic photons from Gamma Ray
Bursts. Then we consider the non-commutative space as a theoretical concept
that could lead to such a deviation, which would be a manifestation of Lorentz
Invariance Violation. In particular we review a numerical study of pure U(1)
gauge theory in a 4d non-commutative space. Starting from a finite lattice, we
explore the phase diagram and the extrapolation to the continuum and infinite
volume. These simultaneous limits - taken at fixed non-commutativity - lead to
a phase of broken Poincare symmetry, where the photon appears to be IR stable,
despite a negative IR divergence to one loop.
