The odd-order Pais-Uhlenbeck oscillator

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    13 Citations (Scopus)


    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 languageEnglish
    Pages (from-to)495-508
    Number of pages14
    JournalNuclear Physics B
    Publication statusPublished - 1 Jun 2016

    ASJC Scopus subject areas

    • Nuclear and High Energy Physics

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