Various disguises of the Pais-Uhlenbeck oscillator

DOI10.1016/J.NUCLPHYSB.2023.116327arXiv2306.06516OpenAlexW4385741540MaRDI QIDQ6095262

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Publication date: 7 September 2023

Published in: (Search for Journal in Brave)

Abstract: Beginning with a simple set of planar equations, we discuss novel realizations of the Pais-Uhlenbeck oscillator in various contexts. First, due to the bi-Hamiltonian character of this model, we develop a Hamiltonian approach for the Eisenhart-Duval lift of the related dynamics. We apply this approach to the previously worked example of a circularly polarized periodic gravitational wave. Then, we present our further results. Firstly, we show that the transverse dynamics of the Lukash plane wave and a complete gravitational wave pulse can also lead to the Pais-Uhlenbeck oscillator. We express the related Carroll Killing vectors in terms of the Pais-Uhlenbeck frequencies and derive extra integrals of motion from the conformal Newton-Hooke symmetry. In addition, we find that the 3+1 dimensional Penning trap can be canonically mapped to the 6th order Pais-Uhlenbeck oscillator. We also carry the problem to the non-commutative plane. Lastly, we discuss other examples like the motion of a charged particle under electromagnetic field created with double copy.

Full work available at URL: https://arxiv.org/abs/2306.06516

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