Realizations of the Yang–Poisson model on canonical phase space

Abstract

In this paper, 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 space–time 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.