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

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dc.creatorDéctor, A.
dc.creatorMorales-Técotl, H. A.
dc.creatorUrrutia, L. F.
dc.creatorVergara, J. D.
dc.date2009-05-05
dc.date.accessioned2026-07-07T13:15:30Z
dc.date.available2026-07-07T13:15:30Z
dc.descriptionOur 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.
dc.identifierhttps://arxiv.org/abs/0905.0589
dc.identifierhttp://arxiv.org/abs/0905.0589
dc.identifierSIGMA.5:053,2009
dc.identifierdoi:10.3842/SIGMA.2009.053
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/230489
dc.subjectMathematical Physics
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Physics
dc.titleAn Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator
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