An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator
Our purpose in this paper is to analyze the Pais-Uhlenbeck (PU) oscillator using complex canonical transformations. We show that starting from a Lagrangian approach we obtain a transformation that makes the extended PU oscillator, with unequal frequencies, to be equivalent to two standard second ord...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2009 |
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| Sprache: | Englisch |
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Інститут математики НАН України
2009
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| Zitieren: | An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator / A. Déctor, H.A. Morales-Técotl, L.F. Urrutia, J.D. Vergara // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 43 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862532426834640896 |
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| author | Déctor, A. Morales-Técotl, H.A. Urrutia, L.F. Vergara, J.D. |
| author_facet | Déctor, A. Morales-Técotl, H.A. Urrutia, L.F. Vergara, J.D. |
| citation_txt | An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator / A. Déctor, H.A. Morales-Técotl, L.F. Urrutia, J.D. Vergara // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 43 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Our purpose in this paper is to analyze the Pais-Uhlenbeck (PU) oscillator using complex canonical transformations. We show that starting from a Lagrangian approach we obtain a transformation that makes the extended PU oscillator, with unequal frequencies, to be equivalent to two standard second order oscillators which have the original number of degrees of freedom. Such extension is provided by adding a total time derivative to the PU Lagrangian together with a complexification of the original variables further subjected to reality conditions in order to maintain the required number of degrees of freedom. The analysis is accomplished at both the classical and quantum levels. Remarkably, at the quantum level the negative norm states are eliminated, as well as the problems of unbounded below energy and non-unitary time evolution. We illustrate the idea of our approach by eliminating the negative norm states in a complex oscillator. Next, we extend the procedure to the Pais-Uhlenbeck oscillator. The corresponding quantum propagators are calculated using Schwinger's quantum action principle. We also discuss the equal frequency case at the classical level.
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| first_indexed | 2025-11-24T04:40:26Z |
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| id | nasplib_isofts_kiev_ua-123456789-149126 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T04:40:26Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
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| spelling | Déctor, A. Morales-Técotl, H.A. Urrutia, L.F. Vergara, J.D. 2019-02-19T17:33:37Z 2019-02-19T17:33:37Z 2009 An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator / A. Déctor, H.A. Morales-Técotl, L.F. Urrutia, J.D. Vergara // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 43 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 70H15; 70H50; 81S10 https://nasplib.isofts.kiev.ua/handle/123456789/149126 Our purpose in this paper is to analyze the Pais-Uhlenbeck (PU) oscillator using complex canonical transformations. We show that starting from a Lagrangian approach we obtain a transformation that makes the extended PU oscillator, with unequal frequencies, to be equivalent to two standard second order oscillators which have the original number of degrees of freedom. Such extension is provided by adding a total time derivative to the PU Lagrangian together with a complexification of the original variables further subjected to reality conditions in order to maintain the required number of degrees of freedom. The analysis is accomplished at both the classical and quantum levels. Remarkably, at the quantum level the negative norm states are eliminated, as well as the problems of unbounded below energy and non-unitary time evolution. We illustrate the idea of our approach by eliminating the negative norm states in a complex oscillator. Next, we extend the procedure to the Pais-Uhlenbeck oscillator. The corresponding quantum propagators are calculated using Schwinger's quantum action principle. We also discuss the equal frequency case at the classical level. This paper is a contribution to the Proceedings of the VIIth Workshop “Quantum Physics with NonHermitian Operators” (June 29 – July 11, 2008, Benasque, Spain). This work was partially supported by the following grants: CONACyT-SEP 51132F, CONACyTSEP 47211-F, CONACyT-SEP 55310, DGAPA-UNAM IN109107 and a CONACyT sabbatical grant to HAMT. AD wishes also to acknowledge support from CONACyT. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator Article published earlier |
| spellingShingle | An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator Déctor, A. Morales-Técotl, H.A. Urrutia, L.F. Vergara, J.D. |
| title | An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator |
| title_full | An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator |
| title_fullStr | An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator |
| title_full_unstemmed | An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator |
| title_short | An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator |
| title_sort | alternative canonical approach to the ghost problem in a complexified extension of the pais-uhlenbeck oscillator |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149126 |
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