Nonstandard Deformed Oscillators from q- and p,q-Deformations of Heisenberg Algebra
For the two-parameter p,q-deformed Heisenberg algebra introduced recently and in which, instead of usual commutator of X and P in the l.h.s. of basic relation [X,P]=iℏ, one uses the p,q-commutator, we established interesting properties. Most important is the realizability of the p,q-deformed Heisenb...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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| Sprache: | Englisch |
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Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147738 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Nonstandard Deformed Oscillators from q- and p,q-Deformations of Heisenberg Algebra / A.M. Gavrilik, I.I. Kachurik // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 38 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862622960679911424 |
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| author | Gavrilik, A.M. Kachurik, I.I. |
| author_facet | Gavrilik, A.M. Kachurik, I.I. |
| citation_txt | Nonstandard Deformed Oscillators from q- and p,q-Deformations of Heisenberg Algebra / A.M. Gavrilik, I.I. Kachurik // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 38 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | For the two-parameter p,q-deformed Heisenberg algebra introduced recently and in which, instead of usual commutator of X and P in the l.h.s. of basic relation [X,P]=iℏ, one uses the p,q-commutator, we established interesting properties. Most important is the realizability of the p,q-deformed Heisenberg algebra by means of the appropriate deformed oscillator algebra. Another uncovered property is special extension of the usual mutual Hermitian conjugation of the creation and annihilation operators, namely the so-called η(N)-pseudo-Hermitian conjugation rule, along with the related η(N)-pseudo-Hermiticity property of the position or momentum operators. In this work, we present some new solutions of the realization problem yielding new (nonstandard) deformed oscillators, and show their inequivalence to the earlier known solution and the respective deformed oscillator algebra, in particular what concerns ground state energy.
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| first_indexed | 2025-12-07T13:27:54Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147738 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T13:27:54Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
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| spelling | Gavrilik, A.M. Kachurik, I.I. 2019-02-15T18:57:44Z 2019-02-15T18:57:44Z 2016 Nonstandard Deformed Oscillators from q- and p,q-Deformations of Heisenberg Algebra / A.M. Gavrilik, I.I. Kachurik // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 38 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R50; 81S05; 81Vxx; 17B37 DOI:10.3842/SIGMA.2016.047 https://nasplib.isofts.kiev.ua/handle/123456789/147738 For the two-parameter p,q-deformed Heisenberg algebra introduced recently and in which, instead of usual commutator of X and P in the l.h.s. of basic relation [X,P]=iℏ, one uses the p,q-commutator, we established interesting properties. Most important is the realizability of the p,q-deformed Heisenberg algebra by means of the appropriate deformed oscillator algebra. Another uncovered property is special extension of the usual mutual Hermitian conjugation of the creation and annihilation operators, namely the so-called η(N)-pseudo-Hermitian conjugation rule, along with the related η(N)-pseudo-Hermiticity property of the position or momentum operators. In this work, we present some new solutions of the realization problem yielding new (nonstandard) deformed oscillators, and show their inequivalence to the earlier known solution and the respective deformed oscillator algebra, in particular what concerns ground state energy. This work was partially supported by the Special Programme of Division of Physics and Astronomy
 of NAS of Ukraine. The authors also thank the anonymous referees for valuable remarks
 that have led to the improved version of the manuscript. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Nonstandard Deformed Oscillators from q- and p,q-Deformations of Heisenberg Algebra Article published earlier |
| spellingShingle | Nonstandard Deformed Oscillators from q- and p,q-Deformations of Heisenberg Algebra Gavrilik, A.M. Kachurik, I.I. |
| title | Nonstandard Deformed Oscillators from q- and p,q-Deformations of Heisenberg Algebra |
| title_full | Nonstandard Deformed Oscillators from q- and p,q-Deformations of Heisenberg Algebra |
| title_fullStr | Nonstandard Deformed Oscillators from q- and p,q-Deformations of Heisenberg Algebra |
| title_full_unstemmed | Nonstandard Deformed Oscillators from q- and p,q-Deformations of Heisenberg Algebra |
| title_short | Nonstandard Deformed Oscillators from q- and p,q-Deformations of Heisenberg Algebra |
| title_sort | nonstandard deformed oscillators from q- and p,q-deformations of heisenberg algebra |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147738 |
| work_keys_str_mv | AT gavrilikam nonstandarddeformedoscillatorsfromqandpqdeformationsofheisenbergalgebra AT kachurikii nonstandarddeformedoscillatorsfromqandpqdeformationsofheisenbergalgebra |