The Weyl-Heisenberg Group on the Noncommutative Two-Torus: A Zoo of Representations
arXiv:0706.3650 · doi:10.1088/1751-8113/40/41/011
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.
24 pages, no figures