The Weyl–Heisenberg group on the noncommutative two-torus: a zoo of representations

2007/06/25 by Jan Govaerts, F. G. Scholtz, Frederik G. Scholtz · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #hep-th

paper · pdf · doi:10.1088/1751-8113/40/41/011

published as J.Phys.A40:12415-12438,2007 · 24 pages, no figures

arxiv created 2007/06/25 · openalex publication_date 2007/09/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

In order to assess possible observable effects of noncommutativity in deformations of quantum mechanics, all irreducible representations of the noncommutative Heisenberg algebra and Weyl–Heisenberg group on the two-torus are constructed. This analysis extends the well-known situation for the noncommutative torus based on the algebra of the noncommuting position operators only. When considering the dynamics of a free particle for any of the identified representations, no observable effect of noncommutativity is implied.

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