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

Govaerts J. ; Scholtz F.G. (2007)


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. © 2007 IOP Publishing Ltd.

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