### Abstract

The method of nonlinear realizations and the technique previously developed in [A. Galajinsky, I. Masterov, Nucl. Phys. B 866 (2013) 212, arXiv:1208.1403] are used to construct a dynamical system without higher derivative terms, which holds invariant under the l-conformal Newton-Hooke group. A configuration space of the model involves coordinates, which parametrize a particle moving in d spatial dimensions and a conformal mode, which gives rise to an effective external field. The dynamical system describes a generalized multi-dimensional oscillator, which undergoes accelerated/decelerated motion in an ellipse in accord with evolution of the conformal mode. Higher derivative formulations are discussed as well. It is demonstrated that the multi-dimensional Pais-Uhlenbeck oscillator enjoys the l=32-conformal Newton-Hooke symmetry for a particular choice of its frequencies.

Original language | English |
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Pages (from-to) | 190-195 |

Number of pages | 6 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 723 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 10 Jun 2013 |

### Keywords

- Conformal Newton-Hooke algebra
- Dynamical realizations
- Pais-Uhlenbeck oscillator

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*,

*723*(1-3), 190-195. https://doi.org/10.1016/j.physletb.2013.04.054