Realizations of the Yang-Poisson model on canonical phase space

TL;DR

This paper explores the classical realization of the Yang-Poisson model, a noncommutative geometric framework with dual position-momentum structures, providing exact solutions in the classical limit.

Contribution

It presents the first explicit realizations of the Yang-Poisson model on canonical phase space, clarifying its classical structure and duality properties.

Findings

Exact realizations of the Yang-Poisson model are constructed.

The classical limit simplifies the noncommutative structure.

Duality between position and momentum manifolds is elucidated.

Abstract

We discuss exact realizations of the Yang-Poisson model on canonical phase space. The Yang model is an example of noncommutative geometry on a background spacetime of constant curvature and is notable for its duality between position and momentum manifolds. We call Yang-Poisson model its classical limit, with commutators replaced by Poisson brackets. The structure is simpler in the classical case, and exact realizations can be found.