The Weyl-Heisenberg Group on the Noncommutative Two-Torus: A Zoo of Representations
Jan Govaerts (1,2), Frederik G. Scholtz (1) ((1) Institute of, Theoretical Physics, Department of Physics, University of Stellenbosch,, Stellenbosch, Republic of South Africa, (2) UNESCO International Chair in, Mathematical Physics, Applications (UNESCO-ICMPA), Cotonou
TL;DR
This paper classifies all irreducible representations of the noncommutative Heisenberg algebra on the two-torus and finds that noncommutativity does not produce observable effects in free particle dynamics.
Contribution
It provides a complete classification of representations of the noncommutative Heisenberg group on the two-torus, extending previous algebraic results.
Findings
No observable effects of noncommutativity in free particle dynamics
Complete set of irreducible representations constructed
Extends known results for noncommutative torus
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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