dorsal/arxiv
View SchemaRepresentations of Coherent States in Non-orthogonal Bases
| Authors | S. Twareque Ali, R. Roknizadeh, M. K. Tavassoly |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0310147 |
| URL | https://arxiv.org/abs/quant-ph/0310147 |
| DOI | 10.1088/0305-4470/37/15/009 |
Abstract
Starting with the canonical coherent states, we demonstrate that all the so-called nonlinear coherent states, used in the physical literature, as well as large classes of other generalized coherent states, can be obtained by changes of bases in the underlying Hilbert space. This observation leads to an interesting duality between pairs of generalized coherent states, bringing into play a Gelfand triple of (rigged) Hilbert spaces. Moreover, it is shown that in each dual pair of families of nonlinear coherent states, at least one family is related to a (generally) non-unitary projective representation of the Weyl-Heisenberg group, which can then be thought of as characterizing the dual pair.
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"abstract": "Starting with the canonical coherent states, we demonstrate that all the\nso-called nonlinear coherent states, used in the physical literature, as well\nas large classes of other generalized coherent states, can be obtained by\nchanges of bases in the underlying Hilbert space. This observation leads to an\ninteresting duality between pairs of generalized coherent states, bringing into\nplay a Gelfand triple of (rigged) Hilbert spaces. Moreover, it is shown that in\neach dual pair of families of nonlinear coherent states, at least one family is\nrelated to a (generally) non-unitary projective representation of the\nWeyl-Heisenberg group, which can then be thought of as characterizing the dual\npair.",
"arxiv_id": "quant-ph/0310147",
"authors": [
"S. Twareque Ali",
"R. Roknizadeh",
"M. K. Tavassoly"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP",
"physics.atom-ph"
],
"doi": "10.1088/0305-4470/37/15/009",
"title": "Representations of Coherent States in Non-orthogonal Bases",
"url": "https://arxiv.org/abs/quant-ph/0310147"
},
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