Remark on a Group-Theoretical Formalism for Quantum Mechanics and the   Quantum-to-Classical Transition
  We sketch a group-theoretical framework, based on the Heisenberg-Weyl group, encompassing both quantum and classical statistical descriptions of mechanical systems. We re-define in group-theoretical terms the kinematical arena and the state-space of the system, achieving a unified quantum-classical language and a novel version of the correspondence principle. We briefly discuss the structure of observables and dynamics within our framework. 
J. K. Korbicz and M. Lewenstein