The Weyl-Heisenberg Group on the Noncommutative Two-Torus: A Zoo of Representations

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.

arXiv comment24 pages, no figures

References in corpus (7)

• Non-commutative Renormalization
• On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
• Quantum Mechanics on the Noncommutative Torus
• Dual families of non-commutative quantum systems
• Interactions and non-commutativity in quantum Hall systems
• Quantum mechanics on noncommutative Riemann surfaces
• Topological Background Fields as Quantum Degrees of Freedom of Compactified Strings

Cited by in corpus (4)

• Spectrum of the non-commutative spherical well
• On the role of twisted statistics in the noncommutative degenerate electron gas
• Free-fall in a uniform gravitational field in non-commutative quantum mechanics
• Bound state energies and phase shifts of a non-commutative well