dorsal/arxiv
View SchemaWigner distributions and quantum mechanics on Lie groups: the case of the regular representation
| Authors | N. Mukunda, Arvind, S. Chaturvedi, R. Simon |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0305012 |
| URL | https://arxiv.org/abs/quant-ph/0305012 |
| DOI | 10.1063/1.1631393 |
Abstract
We consider the problem of setting up the Wigner distribution for states of a quantum system whose configuration space is a Lie group. The basic properties of Wigner distributions in the familiar Cartesian case are systematically generalised to accommodate new features which arise when the configuration space changes from $n$-dimensional Euclidean space ${\cal R}^n$ to a Lie group $G$. The notion of canonical momentum is carefully analysed, and the meanings of marginal probability distributions and their recovery from the Wigner distribution are clarified. For the case of compact $G$ an explicit definition of the Wigner distribution is proposed, possessing all the required properties. Geodesic curves in $G$ which help introduce a notion of the `mid point' of two group elements play a central role in the construction.
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"abstract": "We consider the problem of setting up the Wigner distribution for states of a\nquantum system whose configuration space is a Lie group. The basic properties\nof Wigner distributions in the familiar Cartesian case are systematically\ngeneralised to accommodate new features which arise when the configuration\nspace changes from $n$-dimensional Euclidean space ${\\cal R}^n$ to a Lie group\n$G$. The notion of canonical momentum is carefully analysed, and the meanings\nof marginal probability distributions and their recovery from the Wigner\ndistribution are clarified. For the case of compact $G$ an explicit definition\nof the Wigner distribution is proposed, possessing all the required properties.\nGeodesic curves in $G$ which help introduce a notion of the `mid point\u0027 of two\ngroup elements play a central role in the construction.",
"arxiv_id": "quant-ph/0305012",
"authors": [
"N. Mukunda",
"Arvind",
"S. Chaturvedi",
"R. Simon"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.1631393",
"title": "Wigner distributions and quantum mechanics on Lie groups: the case of the regular representation",
"url": "https://arxiv.org/abs/quant-ph/0305012"
},
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