The Photon Dispersion as an Indicator for New Physics ?

Abstract

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.Comment: 8 pages, 4 figures, talk presented at the VI International Workshop on the Dark Side of the Universe, Leon (Mexico), June 1-6, 2010. References adde