Quantum Mechanics on the Quantum Sphere , 2-3 Quantum Mechanics on the Quantum Sphere

Abstract

A discussion on the quantum mechanics of oneand many-particle systems on the quantum spheres is presented. The role of quantum group symmetry is fully exploited and developed. Generalized dynamical systems are introduced and discussed. We present the concept of generalized homogeneous spaces, and obtain the analogue of topological charges through inequivalent quantizations. The importance and origin of braiding in multi-particle systems is explained. r··· . --. '" -y • """, ".-*r ~·~-~·~ ...-t .... , f l ; j " :. . 1