Conformal Newton–Hooke symmetry of Pais–Uhlenbeck oscillator

2014/02/28 by Krzysztof Andrzejewski, Anton Galajinsky, Joanna Gonera +1
Mathematics · Physics and Astronomy · #Classical mechanics #Conformal map #Conformal symmetry #Geometry #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Symmetry (geometry) #hep-th #math-ph #math.MP

paper · pdf · doi:10.1016/j.nuclphysb.2014.05.025

V3:Introduction extended, one reference added. The version to appear in NPB

openalex publication_date 2014/05/27 · arxiv created 2014/06/03 · arxiv updated 2014/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

It is demonstrated that the Pais–Uhlenbeck oscillator in arbitrary dimension enjoys the l-conformal Newton–Hooke symmetry provided frequencies of oscillation form the arithmetic sequence ωk=(2k−1)ω1, where k=1,…,n, and l is the half-integer 2n−12. The model is shown to be maximally superintegrable. A link to n decoupled isotropic oscillators is discussed and an interplay between the l-conformal Newton–Hooke symmetry and symmetries characterizing each individual isotropic oscillator is analyzed.

Citations

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