Formulation of the Classical Mechanics in the Ring of Operators

A. Vercin

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Formulation of the Classical Mechanics in the Ring of Operators

A. Vercin

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Abstract

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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A. Vercin. 1999-02-18. Formulation of the Classical Mechanics in the Ring of Operators. https://arxiv.org/abs/quant-ph/9902064

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