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arXiv · 2306.06516

Various disguises of the Pais-Uhlenbeck oscillator

Mahmut Elbistan·Krzysztof Andrzejewski
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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.

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Mahmut Elbistan, Krzysztof Andrzejewski. 2023-06-10. Various disguises of the Pais-Uhlenbeck oscillator. https://doi.org/10.1016/j.nuclphysb.2023.116327

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