2016/03/31 by Ivan Masterov · 1 citation
Mathematics · Physics and Astronomy · #Hamiltonian (control theory) #Hamiltonian system #Harmonic oscillator #Invariant (physics) #Lagrangian #Mathematical analysis #Mathematical physics #Mathematics #Noether's theorem #Physics #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum harmonic oscillator #Quantum mechanics #hep-th #math-ph #math.MP
paper · pdf · doi:10.1016/j.nuclphysb.2016.04.025
published as Nucl. Phys. B 907 (2016) 495-508 · V2: 16 pages; references and acknowledgements added, typos corrected. The version to appear in Nucl. Phys. B
openalex publication_date 2016/05/01 · arxiv created 2016/05/13 · arxiv updated 2016/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.