# Time dependent Pais-Uhlenbeck oscillator and its decomposition

@article{Kuwabara2015TimeDP, title={Time dependent Pais-Uhlenbeck oscillator and its decomposition}, author={H. Kuwabara and T. Yumibayashi and H. Harada}, journal={arXiv: General Relativity and Quantum Cosmology}, year={2015} }

The Pais-Uhlenbeck(PU) oscillator is the simplest model with higher time derivatives. Its properties were studied for a long time. In this paper, we extend the 4th order free PU oscillator to a more non-trivial case, dubbed the 4th order time dependent PU oscillator, which has time dependent frequencies. We show that this model cannot be decomposed into two harmonic oscillators in contrast to the original PU oscillator. An interaction is added by the coordinate transformation of Smilga.

#### 2 Citations

Generalized Niederer's transformation for quantum Pais–Uhlenbeck oscillator

- Physics
- 2015

Abstract We extend, to the quantum domain, the results obtained in [Nucl. Phys. B 885 (2014) 150] and [Phys. Lett. B 738 (2014) 405] concerning Niederer's transformation for the Pais–Uhlenbeck… Expand

Nonlocal dynamics and infinite nonrelativistic conformal symmetries

- Physics
- 2016

We study the symmetry of the class of nonlocal models which includes the nonlocal extension of the Pais-Uhlenbeck oscillator. As a consequence, we obtain an infinite dimensional symmetry algebra,… Expand

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