### Abstract

We consider a Hamiltonian formulation of the (2. n+. 1)-order generalization of the Pais-Uhlenbeck oscillator with distinct frequencies of oscillation. This system is invariant under time translations. However, the corresponding Noether integral of motion is unbounded from below and can be presented as a direct sum of 2n one-dimensional harmonic oscillators with an alternating sign. If this integral of motion plays a role of a Hamiltonian, a quantum theory of the Pais-Uhlenbeck oscillator faces a ghost problem. We construct an alternative canonical formulation for the system under study to avoid this nasty feature.

Original language | English |
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Pages (from-to) | 495-508 |

Number of pages | 14 |

Journal | Nuclear Physics B |

Volume | 907 |

DOIs | |

Publication status | Published - 1 Jun 2016 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*907*, 495-508. https://doi.org/10.1016/j.nuclphysb.2016.04.025

**The odd-order Pais-Uhlenbeck oscillator.** / Masterov, Ivan.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 907, pp. 495-508. https://doi.org/10.1016/j.nuclphysb.2016.04.025

}

TY - JOUR

T1 - The odd-order Pais-Uhlenbeck oscillator

AU - Masterov, Ivan

PY - 2016/6/1

Y1 - 2016/6/1

N2 - We consider a Hamiltonian formulation of the (2. n+. 1)-order generalization of the Pais-Uhlenbeck oscillator with distinct frequencies of oscillation. This system is invariant under time translations. However, the corresponding Noether integral of motion is unbounded from below and can be presented as a direct sum of 2n one-dimensional harmonic oscillators with an alternating sign. If this integral of motion plays a role of a Hamiltonian, a quantum theory of the Pais-Uhlenbeck oscillator faces a ghost problem. We construct an alternative canonical formulation for the system under study to avoid this nasty feature.

AB - We consider a Hamiltonian formulation of the (2. n+. 1)-order generalization of the Pais-Uhlenbeck oscillator with distinct frequencies of oscillation. This system is invariant under time translations. However, the corresponding Noether integral of motion is unbounded from below and can be presented as a direct sum of 2n one-dimensional harmonic oscillators with an alternating sign. If this integral of motion plays a role of a Hamiltonian, a quantum theory of the Pais-Uhlenbeck oscillator faces a ghost problem. We construct an alternative canonical formulation for the system under study to avoid this nasty feature.

UR - http://www.scopus.com/inward/record.url?scp=84963821003&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84963821003&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2016.04.025

DO - 10.1016/j.nuclphysb.2016.04.025

M3 - Article

VL - 907

SP - 495

EP - 508

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

ER -