Oscillators from nonlinear realizations
Abstract
We construct the systems of the harmonic and PaisUhlenbeck 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 PaisUhlenbeck oscillators. The firstorder 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.
 Publication:

Journal of Physics Conference Series
 Pub Date:
 February 2018
 DOI:
 10.1088/17426596/965/1/012025
 arXiv:
 arXiv:1710.04937
 Bibcode:
 2018JPhCS.965a2025K
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 9 pages, no figures. To be published in the proceedings of the ISQS25 conference (Prague, 610 June 2017). Includes jpconf.cls and jpconf11.clo