Wigner Quantization of Hamiltonians Describing Harmonic Oscillators Coupled by a General Interaction Matri
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 th...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2009 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149101 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862713670810730496 |
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| author | Regniers, G. Van der Jeugt, Joris |
| author_facet | Regniers, G. Van der Jeugt, Joris |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T17:45:56Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149101 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:45:56Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Regniers, G. Van der Jeugt, Joris 2019-02-19T17:21:53Z 2019-02-19T17:21:53Z 2009 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. 1815-0659 2000 Mathematics Subject Classification: 17B60; 17B80; 81R05; 81R12 https://nasplib.isofts.kiev.ua/handle/123456789/149101 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. G. Regniers was supported by project P6/02 of the Interuniversity Attraction Poles Programme (Belgian State – Belgian Science Policy). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Wigner Quantization of Hamiltonians Describing Harmonic Oscillators Coupled by a General Interaction Matri Article published earlier |
| spellingShingle | Wigner Quantization of Hamiltonians Describing Harmonic Oscillators Coupled by a General Interaction Matri Regniers, G. Van der Jeugt, Joris |
| title | Wigner Quantization of Hamiltonians Describing Harmonic Oscillators Coupled by a General Interaction Matri |
| title_full | Wigner Quantization of Hamiltonians Describing Harmonic Oscillators Coupled by a General Interaction Matri |
| title_fullStr | Wigner Quantization of Hamiltonians Describing Harmonic Oscillators Coupled by a General Interaction Matri |
| title_full_unstemmed | Wigner Quantization of Hamiltonians Describing Harmonic Oscillators Coupled by a General Interaction Matri |
| title_short | Wigner Quantization of Hamiltonians Describing Harmonic Oscillators Coupled by a General Interaction Matri |
| title_sort | wigner quantization of hamiltonians describing harmonic oscillators coupled by a general interaction matri |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149101 |
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