The "Peierls substitution" and the exotic Galilei group

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  • 29 February 2000
Abstract
Owing to the two-parameter central extension of the planar Galilei group, a non relativistic particle in the plane admits an extra structure, which yields noncommuting coordinates. For a particle moving in a magnetic field perpendicular to the plane, the two parameters combine with the magnetic field to provide an effective mass. For vanishing effective mass the phase space admits a two-dimensional reduction, which represents the condensation to collective ``Hall'' motions and justifies the rule called ``Peierls substitution''. Then Geometric Quantization yields the wave functions proposed by Laughlin to describe the Fractional Quantum Hall Effect.

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