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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study the Harmonic and Dirac Oscillator problem extended to athree-dimensional noncom- mutative space where the noncommutativity is inducedby a shift of the dynamical variables with generators of SL(2;R) in a unitaryirreducible representation. The Hilbert space gets the structure of a directproduct with the representation space as a factor, where there exist operatorswhich realize the algebra of Lorentz transformations. The spectrum of thesemodels are considered in perturbation theory, both for small and largenoncommutativity parameters, finding no constraints between coordinates andmomenta noncom- mutativity parameters. Since the representation space of theunitary irreducible representations SL(2;R) can be realized in terms of spacesof square-integrable functions, we conclude that these models are equivalent toquantum mechanical models of particles living in a space with an additionalcompact dimension.  PACS: 03.65.-w; 11.30.Cp; 02.40.Gh

Harmonic and Dirac oscillators in a (2+1)-dimensional noncommutative space