Realization of DSR-relativistic symmetries in Finsler geometries

Abstract

Finsler geometry is a well known generalization of Riemannian geometry which allows to account for a possibly non trivial structure of the space of configurations of relativistic particles. We here establish a link between Finsler geometry and the sort of models with curved momentum space and DSR-relativistic symmetries which have been recently of interest in the quantum-gravity literature. We use as case study the much-studied scenario which is inspired by the $κ$-Poincaré quantum group, and show that the relevant deformation of relativistic symmetries can be implemented within a Finsler geometry.