Oscillators from nonlinear realizations

Abstract

We construct the systems of the harmonic and Pais-Uhlenbeck oscillators, which are invariant with respect to arbitrary noncompact Lie algebras. The equations of motion of these systems can be obtained with the help of the formalism of nonlinear realizations. We prove that it is always possible to choose time and the fields within this formalism in such a way that the equations of motion become linear and, therefore, reduce to ones of ordinary harmonic and Pais-Uhlenbeck oscillators. The first-order actions, that produce these equations, can also be provided. As particular examples of this construction, we discuss the $so(2,3)$ and $G_{2(2)}$ algebras.

9 pages, no figures. To be published in the proceedings of the ISQS25 conference (Prague, 6-10 June 2017). Includes jpconf.cls and jpconf11.clo

References in corpus (5)

• Conformal Newton-Hooke symmetry of Pais-Uhlenbeck oscillator
• Spontaneously Broken Spacetime Symmetries and the Role of Inessential Goldstones
• Minimal realization of $\ell$-conformal Galilei algebra, Pais-Uhlenbeck oscillators and their deformation
• SU(1,2) invariance in two-dimensional oscillator
• Hidden symmetries of deformed oscillators

Cited by in corpus (1)

• Meta-Schrödinger invariance