Conformal Newton-Hooke algebras, Niederer's transformation and Pais-Uhlenbeck oscillator

TL;DR

This paper constructs dynamical systems invariant under l-conformal Newton-Hooke algebras using nonlinear realizations, explores their relation to Galilean symmetries, and develops Niederer's transformation, including an application to the Pais-Uhlenbeck oscillator.

Contribution

It introduces a method to build invariant systems under l-conformal Newton-Hooke algebras and extends Niederer's transformation to relate these systems to Galilei-invariant ones, including an application to Pais-Uhlenbeck oscillators.

Findings

Constructed invariant dynamical systems using nonlinear realizations.

Derived generalized Niederer's transformations relating different symmetry-invariant systems.

Developed an analogue of Niederer's transformation for the Pais-Uhlenbeck oscillator.

Abstract

Dynamical systems invariant under the action of the l-conformal Newton-Hooke algebras are constructed by the method of nonlinear realizations. The relevant first order Lagrangians together with the corresponding Hamiltonians are found. The relation to the Galajinsky and Masterov [Phys. Lett. B 723 (2013) 190] approach as well as the higher derivatives formulation is discussed. The generalized Niederer's transformation are presented which relate the systems under consideration to those invariant under the action of the l-conformal Galilei algebra [Nucl. Phys. B 876 (2013) 309]. As a nice application of these results an analogue of Niederer's transformation, on the Hamiltonian level, for the Pais-Uhlenbeck oscillator is constructed.