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arXiv · hep-th/0002233

The exotic Galilei group and the "Peierls substitution"

C. Duval·P. A. Horváthy
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Abstract

Taking advantage of the two-parameter central extension of the planar Galilei group, we construct a non relativistic particle model in the plane. Owing to the extra structure, the coordinates do not commute. Our model can be viewed as the non-relativistic counterpart of the relativistic anyon considered before by Jackiw and Nair. 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''. Quantization yields the wave functions proposed by Laughlin to describe the Fractional Quantum Hall Effect.

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C. Duval, P. A. Horváthy. 2000-03-14. The exotic Galilei group and the "Peierls substitution". https://doi.org/10.1016/s0370-2693(00)00341-5

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