Generalizations of Snyder model to curved spaces

TL;DR

This paper extends Snyder's algebra to curved spacetimes with de Sitter symmetry, connecting it to Yang model and triply special relativity, and provides explicit realizations in phase space.

Contribution

It introduces generalized Snyder algebras for curved backgrounds and offers explicit phase space realizations, including an exact solution for triply special relativity.

Findings

Unified algebraic framework for Snyder, Yang, and triply special relativity.

Explicit phase space realizations up to fourth order in deformation parameters.

Exact realization of triply special relativity algebra.

Abstract

We consider generalizations of the Snyder algebra to a curved spacetime background with de Sitter symmetry. As special cases, we obtain the algebras of the Yang model and of triply special relativity. We discuss the realizations of these algebras in terms of canonical phase space coordinates, up to fourth order in the deformation parameters. In the case of triply special relativity we also find exact realization, exploiting its algebraic relation with the Snyder model.