English

The odd-order Pais-Uhlenbeck oscillator

Mathematical Physics 2016-05-17 v2 High Energy Physics - Theory math.MP

Abstract

We consider a Hamiltonian formulation of the (2n+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.

Keywords

Cite

@article{arxiv.1603.07727,
  title  = {The odd-order Pais-Uhlenbeck oscillator},
  author = {Ivan Masterov},
  journal= {arXiv preprint arXiv:1603.07727},
  year   = {2016}
}

Comments

V2: 16 pages; references and acknowledgements added, typos corrected. The version to appear in Nucl. Phys. B

R2 v1 2026-06-22T13:18:17.299Z