Quantum and Classical Phase Space: Separability and Entanglement

The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The correspondence between the classical and the quantum criterion of separability for the system is obtained in terms of these functions. Entanglement is generic and separability is special. Some applications are discussed in commonly occuring examples and possibly in exotic systems.