2006/09/30 by Joseph Ben Geloun, Jan Govaerts, Mahouton Norbert Hounkonnou +1 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.1209/0295-5075/80/30001
9 pages, no figures; updated references
arxiv created 2006/11/20 · openalex publication_date 2007/10/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
A ( p , q )-deformation of the Landau problem in a spherically symmetric harmonic potential is considered. The quantum spectrum as well as space noncommutativity are established, whether for the full Landau problem or its quantum Hall projections. The well-known noncommutative geometry in each Landau level is recovered in the appropriate limit p , q =1. However, a novel noncommutative algebra for space coordinates is obtained in the ( p , q )-deformed case, which could also be of interest to collective phenomena in condensed-matter systems.