dorsal/arxiv
View SchemaThe conformally invariant Laplace-Beltrami operator and factor ordering
| Authors | Michael P. Ryan, Jr., Alexander V. Turbiner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0406167 |
| URL | https://arxiv.org/abs/quant-ph/0406167 |
| DOI | 10.1016/j.physleta.2004.10.021 |
| Journal | Phys.Lett. A333 (2004) 30-34 |
Abstract
In quantum mechanics the kinetic energy term for a single particle is usually written in the form of the Laplace-Beltrami operator. This operator is a factor ordering of the classical kinetic energy. We investigate other relatively simple factor orderings and show that the {\it only} other solution for a conformally flat metric is the conformally invariant Laplace-Beltrami operator. For non-conformally-flat metrics this type of factor ordering fails, by just one term, to give the conformally invariant Laplace-Beltrami operator.
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"abstract": "In quantum mechanics the kinetic energy term for a single particle is usually\nwritten in the form of the Laplace-Beltrami operator. This operator is a factor\nordering of the classical kinetic energy. We investigate other relatively\nsimple factor orderings and show that the {\\it only} other solution for a\nconformally flat metric is the conformally invariant Laplace-Beltrami operator.\nFor non-conformally-flat metrics this type of factor ordering fails, by just\none term, to give the conformally invariant Laplace-Beltrami operator.",
"arxiv_id": "quant-ph/0406167",
"authors": [
"Michael P. Ryan, Jr.",
"Alexander V. Turbiner"
],
"categories": [
"quant-ph",
"gr-qc",
"hep-th",
"math-ph",
"math.MP"
],
"doi": "10.1016/j.physleta.2004.10.021",
"journal_ref": "Phys.Lett. A333 (2004) 30-34",
"title": "The conformally invariant Laplace-Beltrami operator and factor ordering",
"url": "https://arxiv.org/abs/quant-ph/0406167"
},
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