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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 053, 22 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.053
(Mi sigma399)
 

This article is cited in 11 scientific papers (total in 11 papers)

An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais–Uhlenbeck Oscillator

A. Déctora, H. A. Morales-Técotlab, L. F. Urrutiaa, J. D. Vergaraa

a Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. Postal 70-543, México D. F., México
b Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, San Rafael Atlixco 186, Col. Vicentina, CP 09340, México D. F., México
References:
Abstract: 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.
Keywords: quantum canonical transformations; higher order derivative models.
Received: November 14, 2008; in final form April 22, 2009; Published online May 5, 2009
Bibliographic databases:
Document Type: Article
MSC: 70H15; 70H50; 81S10
Language: English
Citation: A. Déctor, H. A. Morales-Técotl, L. F. Urrutia, J. D. Vergara, “An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais–Uhlenbeck Oscillator”, SIGMA, 5 (2009), 053, 22 pp.
Citation in format AMSBIB
\Bibitem{DecMorUrr09}
\by A.~D\'ector, H.~A.~Morales-T\'ecotl, L.~F.~Urrutia, J.~D.~Vergara
\paper An Alternative Canonical Approach to the Ghost Problem in a~Complexified Extension of the Pais--Uhlenbeck Oscillator
\jour SIGMA
\yr 2009
\vol 5
\papernumber 053
\totalpages 22
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\crossref{https://doi.org/10.3842/SIGMA.2009.053}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80055088133}
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  • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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