Isotropic representation of noncommutative 2D harmonic oscillator
A.Smailagic, E.Spallucci
TL;DR
This paper demonstrates that a noncommutative 2D harmonic oscillator can be represented isotropically using commutative coordinates, revealing effects similar to magnetic fields and underlying SU(2) symmetry.
Contribution
It introduces an isotropic representation of the noncommutative 2D harmonic oscillator and links noncommutativity effects to magnetic field analogies and SU(2) invariance.
Findings
Noncommutativity induces energy level splitting.
Isotropic representation preserves spectral equivalence.
SU(2) invariance underpins the spectral properties.
Abstract
We show that 2D noncommutative harmonic oscillator has an isotropic representation in terms of commutative coordinates. The noncommutativity in the new mode, induces energy level splitting, and is equivalent to an external magnetic field effect. The equivalence of the spectra of the isotropic and anisotropic representation is traced back to the existence of SU(2) invariance of the noncommutative model.
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