dorsal/arxiv
View SchemaClassical and quantum q-deformed physical systems
| Authors | A. Lavagno, A. M. Scarfone, P. Narayana Swamy |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0605026 |
| URL | https://arxiv.org/abs/quant-ph/0605026 |
| DOI | 10.1140/epjc/s2006-02557-y |
| Journal | Eur.Phys.J.C47:253-261,2006 |
Abstract
On the basis of the non-commutative q-calculus, we investigate a q-deformation of the classical Poisson bracket in order to formulate a generalized q-deformed dynamics in the classical regime. The obtained q-deformed Poisson bracket appears invariant under the action of the q-symplectic group of transformations. In this framework we introduce the q-deformed Hamilton's equations and we derive the evolution equation for some simple q-deformed mechanical systems governed by a scalar potential dependent only on the coordinate variable. It appears that the q-deformed Hamiltonian, which is the generator of the equation of motion, is generally not conserved in time but, in correspondence, a new constant of motion is generated. Finally, by following the standard canonical quantization rule, we compare the well known q-deformed Heisenberg algebra with the algebra generated by the q-deformed Poisson bracket.
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"abstract": "On the basis of the non-commutative q-calculus, we investigate a\nq-deformation of the classical Poisson bracket in order to formulate a\ngeneralized q-deformed dynamics in the classical regime. The obtained\nq-deformed Poisson bracket appears invariant under the action of the\nq-symplectic group of transformations. In this framework we introduce the\nq-deformed Hamilton\u0027s equations and we derive the evolution equation for some\nsimple q-deformed mechanical systems governed by a scalar potential dependent\nonly on the coordinate variable. It appears that the q-deformed Hamiltonian,\nwhich is the generator of the equation of motion, is generally not conserved in\ntime but, in correspondence, a new constant of motion is generated. Finally, by\nfollowing the standard canonical quantization rule, we compare the well known\nq-deformed Heisenberg algebra with the algebra generated by the q-deformed\nPoisson bracket.",
"arxiv_id": "quant-ph/0605026",
"authors": [
"A. Lavagno",
"A. M. Scarfone",
"P. Narayana Swamy"
],
"categories": [
"quant-ph",
"cond-mat.other",
"hep-th",
"math.QA"
],
"doi": "10.1140/epjc/s2006-02557-y",
"journal_ref": "Eur.Phys.J.C47:253-261,2006",
"title": "Classical and quantum q-deformed physical systems",
"url": "https://arxiv.org/abs/quant-ph/0605026"
},
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