Dynamical realizations of l-conformal Newton-Hooke group

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.