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arXiv : hep-th/0002233

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Physics Letters B 479 (2000) 284-290

The exotic Galilei group and the "Peierls substitution"

C. Duval, P. A. Horváthy 1

(2000)

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.

1 :	Laboratoire de Mathématiques et Physique Théorique (LMPT)
	CNRS : UMR6083 – Université François Rabelais - Tours

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:

Mathématiques/Physique mathématique Physique/Physique mathématique Physique/Matière Condensée/Autre Physique/Physique des Hautes Energies - Théorie

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Soumis le : Dimanche 17 Juillet 2005, 15:56:51

Dernière modification le : Dimanche 17 Juillet 2005, 15:56:51