dorsal/arxiv
View SchemaFormulation of the Classical Mechanics in the Ring of Operators
| Authors | A. Vercin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9902064 |
| URL | https://arxiv.org/abs/quant-ph/9902064 |
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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"abstract": "By making use of the Weyl-Wigner-Groenewold-Moyal association rules, a\ncommutative product and a new quantum bracket are constructed in the ring of\noperators \\cal{F}(H). In this way, an isomorphism between Lie algebra of\nclassical observables (with Poisson bracket) and the Lie algebra of quantum\nobservables with this new bracket is established. By these observations, a\nformulation of the classical mechanics in \\cal{F}(H} is obtained and is shown\nto be \\hbar\\to 0 limit of the Heisenberg picture formulation of the quantum\nmechanics.",
"arxiv_id": "quant-ph/9902064",
"authors": [
"A. Vercin"
],
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"quant-ph"
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"title": "Formulation of the Classical Mechanics in the Ring of Operators",
"url": "https://arxiv.org/abs/quant-ph/9902064"
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