Enlarged Galilean symmetry of anyons and the Hall effect

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.

arXiv commentLaTeX, 7 pages. No figures. One more reference added

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• Nonrelativistic anyons in external electromagnetic field
• Semiclassical Dynamics of Electrons in Magnetic Bloch Bands: a Hamiltonian Approach
• Exotic galilean symmetry and non-commutative mechanics
• Non-relativistic symmetries in three space-time dimensions and the Nappi-Witten algebra
• On the Hamiltonian nature of semiclassical equations of motion in the presence of an electromagnetic field and Berry curvature
• Electric Chern-Simons term, enlarged exotic Galilei symmetry and noncommutative plane
• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories
• Statistical Mechanics of an Ideal Gas of Non-Abelian Anyons
• The Maxwell group in 2+1 dimensions and its infinite-dimensional enhancements
• Non-Relativistic Supergeometry in the Moore-Read Fractional Quantum Hall State
• Extended Nappi-Witten Geometry for the Fractional Quantum Hall Effect
• Path-integral quantization of Galilean Fermi fields
• Nonrelativistic Supersymmetry in Noncommutative Space
• Non-constant Non-commutativity in 2d Field Theories and a New Look at Fuzzy Monopoles
• Symmetries of field theories on the non-commutative plane
• (1+1) Newton-Hooke Group for the Simple and Damped Harmonic Oscillator
• Conformal Galilean Spin-3 Gravity in 3d
• Dynamics of semiclassical Bloch wave - packets