A low-energy effective model for spacetime defects and the propagation of photons

Even after several decades of research it has not been clarified how physics at the Planck scale exactly looks like. Since it is a formidable task to find the fundamental theory describing this physics, a reasonable approach is to consider effective theories holding at energies that are much smaller than the Planck energy. We would like to pursue this idea and therefore we construct a simple model of spacetime fluctuations that are referred to as spacetime defects. Such defects are expected to play a major role at the Planck scale where spacetime may not be a smooth entity any more. In our model the spacetime defects are pointlike and they are embedded in Minkowski spacetime according to a Lorentz-invariant sprinkling process. The question is how the propagation of photons is influenced by such spacetime defects, i.e. whether Lorentz invariance still holds. The photon is assumed not to interact directly with the defects, but the interaction is mediated by a scalar field. The interesting result is that under certain further assumptions the photon does not feel the defects and the photon dispersion relation remains standard. In this talk the model, the calculational methods, and the result are presented and discussed.