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

• Main Author: Krzysztof Andrzejewski
• Format: Article
• Language: English
• Published: Elsevier 2014-11-01
• Series: Physics Letters B
• Online Access: http://www.sciencedirect.com/science/article/pii/S037026931400731X

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 [24] approach as well as the higher derivatives formulation is discussed. The generalized Niederer's transformation is presented which relates the systems under consideration to those invariant under the action of the l-conformal Galilei algebra [25]. As a nice application of these results an analogue of Niederer's transformation, on the Hamiltonian level, for the Pais–Uhlenbeck oscillator is constructed.