Dissipation and Noncommutativity in Planar Quantum Mechanics

Noncommutative algebra in planar quantum mechanics is shown to follow from ’t Hooft’s recent analysis on dissipation and quantization. The noncommutativity in the coordinates or in the momenta of a charged particle in a magnetic field with an oscillator potential are shown as dual descriptions of the same phenomenon. Finally, noncommutativity in a fluid dynamical model, analogous to the lowest Landau level problem, is discussed.