dorsal/arxiv
View SchemaGeneralized Weyl-Wigner map and Vey quantum mechanics
| Authors | Nuno Costa Dias, Joao Nuno Prata |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0102018 |
| URL | https://arxiv.org/abs/quant-ph/0102018 |
| DOI | 10.1063/1.1415086 |
| Journal | J. Math. Phys. 42 (2001) 5565-5579 |
Abstract
The Weyl-Wigner map yields the entire structure of Moyal quantum mechanics directly from the standard operator formulation. The covariant generalization of Moyal theory, also known as Vey quantum mechanics, was presented in the literature many years ago. However, a derivation of the formalism directly from standard operator quantum mechanics, clarifying the relation between the two formulations is still missing. In this paper we present a covariant generalization of the Weyl order prescription and of the Weyl-Wigner map and use them to derive Vey quantum mechanics directly from the standard operator formulation. The procedure displays some interesting features: it yields all the key ingredients and provides a more straightforward interpretation of the Vey theory including a direct implementation of unitary operator transformations as phase space coordinate transformations in the Vey idiom. These features are illustrated through a simple example.
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"abstract": "The Weyl-Wigner map yields the entire structure of Moyal quantum mechanics\ndirectly from the standard operator formulation. The covariant generalization\nof Moyal theory, also known as Vey quantum mechanics, was presented in the\nliterature many years ago. However, a derivation of the formalism directly from\nstandard operator quantum mechanics, clarifying the relation between the two\nformulations is still missing. In this paper we present a covariant\ngeneralization of the Weyl order prescription and of the Weyl-Wigner map and\nuse them to derive Vey quantum mechanics directly from the standard operator\nformulation. The procedure displays some interesting features: it yields all\nthe key ingredients and provides a more straightforward interpretation of the\nVey theory including a direct implementation of unitary operator\ntransformations as phase space coordinate transformations in the Vey idiom.\nThese features are illustrated through a simple example.",
"arxiv_id": "quant-ph/0102018",
"authors": [
"Nuno Costa Dias",
"Joao Nuno Prata"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.1415086",
"journal_ref": "J. Math. Phys. 42 (2001) 5565-5579",
"title": "Generalized Weyl-Wigner map and Vey quantum mechanics",
"url": "https://arxiv.org/abs/quant-ph/0102018"
},
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