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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| Дата: | 2009 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2009
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149126 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1491262019-02-20T01:27:49Z 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. 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. 2009 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149126 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Déctor, A. Morales-Técotl, H.A. Urrutia, L.F. Vergara, J.D. |
| spellingShingle |
Déctor, A. Morales-Técotl, H.A. Urrutia, L.F. Vergara, J.D. An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Déctor, A. Morales-Técotl, H.A. Urrutia, L.F. Vergara, J.D. |
| author_sort |
Déctor, A. |
| title |
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_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_sort |
alternative canonical approach to the ghost problem in a complexified extension of the pais-uhlenbeck oscillator |
| publisher |
Інститут математики НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149126 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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