The odd-order Pais-Uhlenbeck oscillator

Ivan Masterov

    Research output: Contribution to journalArticle

    10 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)495-508
    Number of pages14
    JournalNuclear Physics B
    Volume907
    DOIs
    Publication statusPublished - 1 Jun 2016

    Fingerprint

    oscillators
    formulations
    ghosts
    quantum theory
    harmonic oscillators
    oscillations

    ASJC Scopus subject areas

    • Nuclear and High Energy Physics

    Cite this

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

    In: Nuclear Physics B, Vol. 907, 01.06.2016, p. 495-508.

    Research output: Contribution to journalArticle

    Masterov, Ivan. / The odd-order Pais-Uhlenbeck oscillator. In: Nuclear Physics B. 2016 ; Vol. 907. pp. 495-508.
    @article{c2f46a00a4774d568e9fdba6dd75252f,
    title = "The odd-order Pais-Uhlenbeck oscillator",
    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.",
    author = "Ivan Masterov",
    year = "2016",
    month = "6",
    day = "1",
    doi = "10.1016/j.nuclphysb.2016.04.025",
    language = "English",
    volume = "907",
    pages = "495--508",
    journal = "Nuclear Physics B",
    issn = "0550-3213",
    publisher = "Elsevier",

    }

    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 -