The " Peierls Substitution " and the Exotic Galilei Group
نویسندگان
چکیده
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 noncom-muting 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.
منابع مشابه
2 Exotic particle in the plane
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 pl...
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