Classical and quantum mechanics of the nonrelativistic Snyder model in curved space

Understand

The Snyder-de Sitter (SdS) model is a generalization of the Snyder model to a spacetime background of constant curvature.

• It is an example of noncommutative spacetime admitting two fundamental scales besides the speed of light, and is invariant under the action of the de Sitter group.
• Here we consider its nonrelativistic counterpart, i.e.
• the Snyder model restricted to a three-dimensional sphere, and the related model obtained by considering the anti-Snyder model on a pseudosphere, that we call anti-Snyder-de Sitter (aSdS).