### 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 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

Masterov, I. (2016). The odd-order Pais-Uhlenbeck oscillator.

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