Hidden symmetries of deformed oscillators

Abstract

We associate with each simple Lie algebra a system of second-order differential equations invariant under a non-compact real form of the corresponding Lie group. In the limit of a contraction to a Schrödinger algebra, these equations reduce to a system of ordinary harmonic oscillators. We provide two clarifying examples of such deformed oscillators: one system invariant under SO(2,3) transformations, and another system featuring $G_{2(2)}$ symmetry. The construction of invariant actions requires adding semi-dynamical degrees of freedom; we illustrate the algorithm with the two examples mentioned.

1+10 pages

References in corpus (3)

• Supersymmetric Calogero models by gauging
• Conformal Newton-Hooke symmetry of Pais-Uhlenbeck oscillator
• Dynamical realizations of N=1 l-conformal Galilei superalgebra

Cited by in corpus (2)

• Schrödinger symmetry: a historical review
• Oscillators from nonlinear realizations