a Department of Physics, Rockefeller University, New York, NY 10021, USA
b Department of Physics, City College of the CUNY, New York, NY 10031, USA
c Department of Physics, Columbia University, New York, NY 10027, USA
Abstract:
We analyze the algebra of observables of a charged particle on a noncommutative torus in a constant magnetic field. We present a set of generators of this algebra which coincide with the generators for a commutative torus but at a different value of the magnetic field, and demonstrate the existence of a critical value of the magnetic field for which the algebra reduces. We then obtain the irreducible representations of the algebra and relate them to noncommutative bundles. Finally we comment on Landau levels, density of states and the critical case.