Classical dynamics on curved Snyder space

TL;DR

This paper investigates classical particle dynamics in curved Snyder space, providing a reduction to classical mechanics for symmetric systems and extending the analysis to relativistic and flat space cases.

Contribution

It introduces a method to analyze classical dynamics in curved Snyder space and extends the framework to relativistic and flat space scenarios.

Findings

Reduction of the problem to classical mechanics for symmetric systems

Extension of results to relativistic dynamics

Generalization to flat space algebra

Abstract

We study the classical dynamics of a particle in nonrelativistic Snyder-de Sitter space. We show that for spherically symmetric systems, parametrizing the solutions in terms of an auxiliary time variable, which is a function only of the physical time and of the energy and angular momentum of the particles, one can reduce the problem to the equivalent one in classical mechanics. We also discuss a relativistic extension of these results, and a generalization to the case in which the algebra is realized in flat space.