Formulation of the Classical Mechanics in the Ring of Operators

Details Formulation of the Classical Mechanics in the Ring of Operators Formulation of the Classical Mechanics in the Ring of Operators

1999-02-18

arxiv.org/abs/quant-ph/9902064v1

Physics

Quantum Physics

14 Pages

Scientific paper

By making use of the Weyl-Wigner-Groenewold-Moyal association rules, a commutative product and a new quantum bracket are constructed in the ring of operators \cal{F}(H). In this way, an isomorphism between 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 the classical mechanics in \cal{F}(H} is obtained and is shown to be \hbar\to 0 limit of the Heisenberg picture formulation of the quantum mechanics.

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