dorsal/arxiv
View SchemaCoherent states on spheres
| Authors | Brian C. Hall, Jeffrey J. Mitchell |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0109086 |
| URL | https://arxiv.org/abs/quant-ph/0109086 |
| DOI | 10.1063/1.1446664 |
| Journal | J.Math.Phys. 43 (2002) 1211-1236; Erratum-ibid. 46 (2005) 059901 |
Abstract
We describe a family of coherent states and an associated resolution of the identity for a quantum particle whose classical configuration space is the d-dimensional sphere S^d. The coherent states are labeled by points in the associated phase space T*(S^d). These coherent states are NOT of Perelomov type but rather are constructed as the eigenvectors of suitably defined annihilation operators. We describe as well the Segal-Bargmann representation for the system, the associated unitary Segal-Bargmann transform, and a natural inversion formula. Although many of these results are in principle special cases of the results of B. Hall and M. Stenzel, we give here a substantially different description based on ideas of T. Thiemann and of K. Kowalski and J. Rembielinski. All of these results can be generalized to a system whose configuration space is an arbitrary compact symmetric space. We focus on the sphere case in order to be able to carry out the calculations in a self-contained and explicit way.
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"abstract": "We describe a family of coherent states and an associated resolution of the\nidentity for a quantum particle whose classical configuration space is the\nd-dimensional sphere S^d. The coherent states are labeled by points in the\nassociated phase space T*(S^d). These coherent states are NOT of Perelomov type\nbut rather are constructed as the eigenvectors of suitably defined annihilation\noperators. We describe as well the Segal-Bargmann representation for the\nsystem, the associated unitary Segal-Bargmann transform, and a natural\ninversion formula. Although many of these results are in principle special\ncases of the results of B. Hall and M. Stenzel, we give here a substantially\ndifferent description based on ideas of T. Thiemann and of K. Kowalski and J.\nRembielinski. All of these results can be generalized to a system whose\nconfiguration space is an arbitrary compact symmetric space. We focus on the\nsphere case in order to be able to carry out the calculations in a\nself-contained and explicit way.",
"arxiv_id": "quant-ph/0109086",
"authors": [
"Brian C. Hall",
"Jeffrey J. Mitchell"
],
"categories": [
"quant-ph",
"gr-qc",
"hep-th",
"math-ph",
"math.MP"
],
"doi": "10.1063/1.1446664",
"journal_ref": "J.Math.Phys. 43 (2002) 1211-1236; Erratum-ibid. 46 (2005) 059901",
"title": "Coherent states on spheres",
"url": "https://arxiv.org/abs/quant-ph/0109086"
},
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