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

Source: [Conformal Newton-Hooke algebras, Niederer's transformation and Pais-Uhlenbeck oscillator](<https://www.sota2.com/research/paper/68fa32b61e209131ce88a250>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T19:39:15.235Z

Authors: K. Andrzejewski

Published: 2014-09-13T08:13:28.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1409.3926>)

[PDF](<https://arxiv.org/pdf/1409.3926.pdf>)