Dynamical realizations of l-conformal Newton-Hooke group

TL;DR

This paper constructs a new dynamical system invariant under the l-conformal Newton-Hooke group using nonlinear realizations, describing a generalized oscillator with accelerated motion and exploring higher derivative formulations.

Contribution

It introduces a novel method to realize the l-conformal Newton-Hooke symmetry in a non-higher-derivative dynamical system and connects it to multi-dimensional oscillators.

Findings

The system models a particle in d dimensions with a conformal mode affecting its motion.

The multi-dimensional Pais-Uhlenbeck oscillator exhibits l=3/2-conformal Newton-Hooke symmetry for specific frequencies.

Higher derivative formulations of the system are also discussed.

Abstract

The method of nonlinear realizations and the technique previously developed in 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=3/2-conformal Newton-Hooke symmetry for a particular choice of its frequencies.