Quantum mechanics on the noncommutative torus

2001/02/28 by Bogdan Morariu, Alexios P. Polychronakos · 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:10.1016/s0550-3213(01)00294-2

published as Nucl.Phys. B610 (2001) 531-544 · LaTeX, 19 pages, no figures, references added

arxiv created 2001/05/21 · openalex publication_date 2001/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze the algebra of observables of a charged particle on a noncommutative torus in a constant magnetic field. We present a set of generators of this algebra which coincide with the generators for a commutative torus but at a different value of the magnetic field, and demonstrate the existence of a critical value of the magnetic field for which the algebra reduces. We then obtain the irreducible representations of the algebra and relate them to noncommutative bundles. Finally we comment on Landau levels, density of states and the critical case.

Citations

• Quantum Mechanics on the Hypercube
• The Quantum Hall Fluid and Non-Commutative Chern Simons Theory
• Dualities of the matrix model from T-duality of the Type II string
• Mtheory as a matrix model: A conjecture
• Hydrogen Atom Spectrum and the Lamb Shift in Noncommutative QED
• Noncommutative quantum mechanics
• “Peierls substitution” and Chern-Simons Quantum mechanics
• The M(atrix) model of M-theory

Cited by

• Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces
• Noncommutative Classical Mechanics