dorsal/arxiv
View SchemaWigner-Weyl isomorphism for quantum mechanics on Lie groups
| Authors | N. Mukunda, G. Marmo, Alessandro Zampini, S. Chaturvedi, R. Simon |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0407257 |
| URL | https://arxiv.org/abs/quant-ph/0407257 |
| DOI | 10.1063/1.1825078 |
| Journal | J.Math.Phys. 46 (2005) 012106 |
Abstract
The Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group $G$ is developed in detail. Several New features are shown to arise which have no counterparts in the familiar Cartesian case. Notable among these is the notion of a `semiquantised phase space', a structure on which the Weyl symbols of operators turn out to be naturally defined and, figuratively speaking, located midway between the classical phase space $T^*G$ and the Hilbert space of square integrable functions on $G$. General expressions for the star product for Weyl symbols are presented and explicitly worked out for the angle-angular momentum case.
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"abstract": "The Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie\ngroup $G$ is developed in detail. Several New features are shown to arise which\nhave no counterparts in the familiar Cartesian case. Notable among these is the\nnotion of a `semiquantised phase space\u0027, a structure on which the Weyl symbols\nof operators turn out to be naturally defined and, figuratively speaking,\nlocated midway between the classical phase space $T^*G$ and the Hilbert space\nof square integrable functions on $G$. General expressions for the star product\nfor Weyl symbols are presented and explicitly worked out for the angle-angular\nmomentum case.",
"arxiv_id": "quant-ph/0407257",
"authors": [
"N. Mukunda",
"G. Marmo",
"Alessandro Zampini",
"S. Chaturvedi",
"R. Simon"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.1825078",
"journal_ref": "J.Math.Phys. 46 (2005) 012106",
"title": "Wigner-Weyl isomorphism for quantum mechanics on Lie groups",
"url": "https://arxiv.org/abs/quant-ph/0407257"
},
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