SU(1,2) invariance in two-dimensional oscillator

TL;DR

This paper demonstrates that a deformed two-dimensional oscillator with SU(1,2) symmetry is canonically equivalent to the ordinary oscillator, revealing SU(1,2) as its dynamical symmetry with non-polynomial generators.

Contribution

It establishes the canonical equivalence between a deformed oscillator and the ordinary one, and identifies SU(1,2) as the dynamical symmetry with a unique non-polynomial structure.

Findings

Proved the canonical equivalence of the deformed and ordinary oscillators.

Identified SU(1,2) as the dynamical symmetry of the oscillator.

Showed the non-polynomial structure of the SU(1,2) generators.

Abstract

Performing the Hamiltonian analysis we explicitly established the canonical equivalence of the deformed oscillator, constructed in arXiv:1607.03756[hep-th], with the ordinary one. As an immediate consequence, we proved that the SU(1,2) symmetry is the dynamical symmetry of the ordinary two-dimensional oscillator. The characteristic feature of this SU(1,2) symmetry is a non-polynomial structure of its generators written it terms of the oscillator variables.