dorsal/arxiv
View SchemaOn the deformability of Heisenberg algebras
| Authors | Mathias Pillin |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9508014 |
| URL | https://arxiv.org/abs/q-alg/9508014 |
| DOI | 10.1007/BF02101181 |
| Journal | Commun. Math. Phys. 180 (1996) 23 |
Abstract
Based on the vanishing of the second Hochschild cohomology group of the enveloping algebra of the Heisenberg algebra it is shown that differential algebras coming from quantum groups do not provide a non-trivial deformation of quantum mechanics. For the case of a q-oscillator there exists a deforming map to the classical algebra. It is shown that the differential calculus on quantum planes with involution, i.e. if one works in position-momentum realization, can be mapped on a q-difference calculus on a commutative real space. Although this calculus leads to an interesting discretization it is proved that it can be realized by generators of the undeformed algebra and does not posess a proper group of global transformations.
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"abstract": "Based on the vanishing of the second Hochschild cohomology group of the\nenveloping algebra of the Heisenberg algebra it is shown that differential\nalgebras coming from quantum groups do not provide a non-trivial deformation of\nquantum mechanics. For the case of a q-oscillator there exists a deforming map\nto the classical algebra. It is shown that the differential calculus on quantum\nplanes with involution, i.e. if one works in position-momentum realization, can\nbe mapped on a q-difference calculus on a commutative real space. Although this\ncalculus leads to an interesting discretization it is proved that it can be\nrealized by generators of the undeformed algebra and does not posess a proper\ngroup of global transformations.",
"arxiv_id": "q-alg/9508014",
"authors": [
"Mathias Pillin"
],
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"q-alg",
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],
"doi": "10.1007/BF02101181",
"journal_ref": "Commun. Math. Phys. 180 (1996) 23",
"title": "On the deformability of Heisenberg algebras",
"url": "https://arxiv.org/abs/q-alg/9508014"
},
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