dorsal/arxiv
View SchemaAlternative commutation relations, star products and tomography
| Authors | Olga V. Man'ko, V. I. Man'ko, G. Marmo |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0112110 |
| URL | https://arxiv.org/abs/quant-ph/0112110 |
| DOI | 10.1088/0305-4470/35/3/315 |
Abstract
Invertible maps from operators of quantum obvservables onto functions of c-number arguments and their associative products are first assessed. Different types of maps like Weyl-Wigner-Stratonovich map and s-ordered quasidistribution are discussed. The recently introduced symplectic tomography map of observables (tomograms) related to the Heisenberg-Weyl group is shown to belong to the standard framework of the maps from quantum observables onto the c-number functions. The star-product for symbols of the quantum-observable for each one of the maps (including the tomographic map) and explicit relations among different star-products are obtained. Deformations of the Moyal star-product and alternative commutation relations are also considered.
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"abstract": "Invertible maps from operators of quantum obvservables onto functions of\nc-number arguments and their associative products are first assessed. Different\ntypes of maps like Weyl-Wigner-Stratonovich map and s-ordered quasidistribution\nare discussed. The recently introduced symplectic tomography map of observables\n(tomograms) related to the Heisenberg-Weyl group is shown to belong to the\nstandard framework of the maps from quantum observables onto the c-number\nfunctions. The star-product for symbols of the quantum-observable for each one\nof the maps (including the tomographic map) and explicit relations among\ndifferent star-products are obtained. Deformations of the Moyal star-product\nand alternative commutation relations are also considered.",
"arxiv_id": "quant-ph/0112110",
"authors": [
"Olga V. Man\u0027ko",
"V. I. Man\u0027ko",
"G. Marmo"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/35/3/315",
"title": "Alternative commutation relations, star products and tomography",
"url": "https://arxiv.org/abs/quant-ph/0112110"
},
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