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dc.contributor.author |
Regniers, G. |
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dc.contributor.author |
Van der Jeugt, Joris |
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dc.date.accessioned |
2019-02-19T17:21:53Z |
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dc.date.available |
2019-02-19T17:21:53Z |
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dc.date.issued |
2009 |
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dc.identifier.citation |
Wigner Quantization of Hamiltonians Describing Harmonic Oscillators Coupled by a General Interaction Matri / G. Regniers, Joris Van der Jeugt // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 21 назв. — англ. |
uk_UA |
dc.identifier.issn |
1815-0659 |
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dc.identifier.other |
2000 Mathematics Subject Classification: 17B60; 17B80; 81R05; 81R12 |
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dc.identifier.uri |
http://dspace.nbuv.gov.ua/handle/123456789/149101 |
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dc.description.abstract |
In a system of coupled harmonic oscillators, the interaction can be represented by a real, symmetric and positive definite interaction matrix. The quantization of a Hamiltonian describing such a system has been done in the canonical case. In this paper, we take a more general approach and look at the system as a Wigner quantum system. Hereby, one does not assume the canonical commutation relations, but instead one just requires the compatibility between the Hamilton and Heisenberg equations. Solutions of this problem are related to the Lie superalgebras gl(1|n) and osp(1|2n). We determine the spectrum of the considered Hamiltonian in specific representations of these Lie superalgebras and discuss the results in detail. We also make the connection with the well-known canonical case. |
uk_UA |
dc.description.sponsorship |
G. Regniers was supported by project P6/02 of the Interuniversity Attraction Poles Programme (Belgian State – Belgian Science Policy). |
uk_UA |
dc.language.iso |
en |
uk_UA |
dc.publisher |
Інститут математики НАН України |
uk_UA |
dc.relation.ispartof |
Symmetry, Integrability and Geometry: Methods and Applications |
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dc.title |
Wigner Quantization of Hamiltonians Describing Harmonic Oscillators Coupled by a General Interaction Matri |
uk_UA |
dc.type |
Article |
uk_UA |
dc.status |
published earlier |
uk_UA |
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