Realization of DSR-relativistic symmetries in Finsler geometries

TL;DR

This paper demonstrates how Finsler geometry can model DSR-relativistic symmetries, linking curved momentum space concepts from quantum gravity to geometric frameworks.

Contribution

It establishes a connection between Finsler geometry and models with curved momentum space exhibiting DSR-relativistic symmetries, especially inspired by the $ ext{kappa}$-Poincaré quantum group.

Findings

Finsler geometry can encode DSR-relativistic symmetries.

Deformations of relativistic symmetries are realizable within Finsler frameworks.

The approach bridges quantum gravity models with geometric descriptions.

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 $\kappa$-Poincar\'e quantum group, and show that the relevant deformation of relativistic symmetries can be implemented within a Finsler geometry.