Operator formulation of classical mechanics

By making use of the Weyl-Wigner-Groenewold-Moyal association rules, a commutative product and a new quantum bracket are constructed in the space of operators F(H). In this way, an isomorphism between the Lie algebra of classical observables (with Poisson bracket) and the Lie algebra of quantum observables with this new bracket is established. By these observations, a formulation of classical mechanics in F(H) is obtained and is shown to be the h --> 0 limit of the Heisenberg-picture formulation of quantum mechanics.