Relative-locality phenomenology on Snyder spacetime

Abstract

We study the effects of relative locality dynamics in the case of the Snyder model. Several properties of this model differ from those of the widely studied $\kappa$-Poincar\'e models: for example, in the Snyder case the action of the Lorentz group is preserved, and the composition law of momenta is deformed by terms quadratic in the inverse Planck energy. From the investigation of time delay and dual curvature lensing we deduce that, because of these differences, in the Snyder case the properties of the detector are essential for the observation of relative locality effects. The deviations from special relativity do not depend on the energy of the particles and are much smaller than in the $\kappa$-Poincar\'e case, so that are beyond the reach of present astrophysical experiments. However, these results have a conceptual interest, because they show that relative-locality effects can occur even if the action of the Lorentz group on phase space is not deformed.