Remark on higher-derivative mechanics with l-conformal Galilei symmetry

TL;DR

This paper constructs a higher-derivative mechanical model with l-conformal Galilei symmetry, extending previous work to include a generalized Pais-Uhlenbeck oscillator influenced by an external field.

Contribution

It introduces a new higher-derivative model exhibiting l-conformal Galilei symmetry, expanding the class of symmetric dynamical systems.

Findings

Model generalizes Pais-Uhlenbeck oscillator

Incorporates an effective external field

Maintains l-conformal Galilei symmetry

Abstract

Based on the results in [Nucl. Phys. B 866 (2013) 212], we consider a way to construct a higher-derivative mechanical model which possesses the $l$-conformal Galilei symmetry. The dynamical system describes generalized Pais-Uhlenbeck oscillator in the presence of an effective external field.