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 unconstrained, non-relativistic mechanical systems. We redefine in group-theoretical terms a kinematical arena and a space of statistical states of a system, achieving a unified quantum-classical language and an elegant version of the quantum-to-classical transition. We briefly discuss the structure of observables and dynamics within our framework.