English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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

Oscillators from nonlinear realizations