Enlarged Galilean symmetry of anyons and the Hall effect

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Abstract

Enlarged planar Galilean symmetry, built of both space-time and field variables and also incorporating the "exotic" central extension is introduced. It is used to describe non-relativistic anyons coupled to an electromagnetic field. Our theory exhibits an anomalous velocity relation of the type used to explain the anomalous Hall effect. The Hall motions, characterized by a Casimir of the enlarged algebra, become mandatory for some critical value(s) of the magnetic field. The extension of our scheme yields the semiclassical effective model of the Bloch electron. © 2005 Elsevier B.V. All rights reserved.

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Horváthy, P. A., Martina, L., & Stichel, P. C. (2005). Enlarged Galilean symmetry of anyons and the Hall effect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 615(1–2), 87–92. https://doi.org/10.1016/j.physletb.2005.04.004

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