Dynamical realization of l-conformal Galilei algebra and oscillators

TL;DR

This paper uses nonlinear realizations to construct a dynamical system based on the l-conformal Galilei algebra, resulting in a model that maps particle trajectories to decoupled oscillators without higher derivatives.

Contribution

It introduces a novel approach to realize the l-conformal Galilei algebra dynamically, avoiding higher derivatives and linking particle trajectories to decoupled oscillators.

Findings

Trajectories can be mapped to decoupled oscillators

The model involves a conformal mode acting as an external field

No higher derivative terms in equations of motion

Abstract

The method of nonlinear realizations is applied to the l-conformal Galilei algebra to construct a dynamical system without higher derivative terms in the equations of motion. A configuration space of the model involves coordinates, which parametrize particles in d spatial dimensions, and a conformal mode, which gives rise to an effective external field. It is shown that trajectories of the system can be mapped into those of a set of decoupled oscillators in d dimensions.