Could the photon dispersion relation be non-linear ?

Abstract

The free photon dispersion relation is a reference quantity for high precision tests of Lorentz Invariance. We first outline theoretical approaches to a conceivable Lorentz Invariance Violation (LIV). Next we address phenomenological tests based on the propagation of cosmic rays, in particular in Gamma Ray Bursts (GRBs). As a specific concept, which could imply LIV, we then focus on field theory in a non-commutative (NC) space, and we present non-perturbative results for the dispersion relation of the NC photon.Comment: 9 pages, 5 figures, talk presented at the 4. EU RTN Workshop on "Constituents, Fundamental Forces and Symmetries of the Universe" in Varna, Sept. 2008. References adde