Nonrelativistic anyons in external electromagnetic field

Abstract

The first-order, infinite-component field equations we proposed before for non-relativistic anyons (identified with particles in the plane with noncommuting coordinates) are generalized to accommodate arbitrary background electromagnetic fields. Consistent coupling of the underlying classical system to arbitrary fields is introduced; at a critical value of the magnetic field, the particle follows a Hall-like law of motion. The corresponding quantized system reveals a hidden nonlocality if the magnetic field is inhomogeneous. In the quantum Landau problem spectral as well as state structure (finite vs. infinite) asymmetry is found. The bound and scattering states, separated by the critical magnetic field phase, behave as further, distinct phases.

19 pages, typos corrected; to appear in Nucl. Phys. B

References in corpus (24)

• The exotic Galilei group and the "Peierls substitution"
• Exotic galilean symmetry in the non-commutative plane, and the Hall effect
• Galilean-Invariant (2+1)-Dimensional Models with a Chern-Simons-Like Term and D=2 N oncommutative Geometry
• Deformed Heisenberg algebra, fractional spin fields and supersymmetry without fermions
• Two phases of the noncommutative quantum mechanics
• The non-commutative Landau problem
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• Non-relativistic anyons, exotic Galilean symmetry and noncommutative plane
• The Projective Unitary Irreducible Representations of the Galilei Group in 1+2 Dimensions
• Anyons as spinning particles
• The Projective Unitary Irreducible Representations of the Poincaré Group in 1+2 Dimensions
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• Galilean invariance in 2+1 dimensions
• Anyons with anomalous gyromagnetic ratio & the Hall effect
• Noncommutative Chern-Simons Solitons
• Noncommutative Planar Particle Dynamics with Gauge Interactions
• Anyons in Electromagnetic Field and the BMT Equation
• Enlarged Galilean symmetry of anyons and the Hall effect
• Dirac versus reduced phase space quantization for systems admitting no gauge conditions
• Self-dual Chern-Simons solitons in noncommutative space
• Linear Differential Equations for a Fractional Spin Field
• Deformed Chern-Simons interaction for nonrelativistic point particles
• A novel BRST approach in generalizing the Jackiw-Nair anyon

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• Noncommutative Quantum Hall Effect and Aharonov-Bohm Effect
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• Exotic galilean symmetry and non-commutative mechanics
• Newton-Hooke type symmetry of anisotropic oscillators
• Super-extended noncommutative Landau problem and conformal symmetry
• Electric Chern-Simons term, enlarged exotic Galilei symmetry and noncommutative plane
• Chiral decomposition in the non-commutative Landau problem
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• Kohn condition and exotic Newton-Hooke symmetry in the non-commutative Landau problem
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• Exotic Hill Problem: Hall motions and symmetries
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• Entanglement of higher-derivative oscillators in holographic systems
• Canonical Structure of Noncommutative Quantum Mechanics as Constraint System
• Noncommutative Geometry and Deformation Quantization in the Quantum Hall Fluids with Inhomogeneous Magnetic Fields
• Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane
• Spontaneous symmetry breaking and masses numerical results in DFR noncommutative space-time
• Quantization of soluble classical constrained systems
• Weak-strong duality of the non-commutative Landau problem induced by a two-vortex permutation, and conformal bridge transformation
• Exotic Non-relativistic String
• Gauge invariance and classical dynamics of noncommutative particle theory
• Quantum dot with spin-orbit interaction in noncommutative phase space and analog Landau levels
• Two-dimensional Noncommutative atom Gas with Anandan interaction
• N=2 supersymmetric odd-order Pais-Uhlenbeck oscillator
• A general relativity formulation for the Doplicher-Fredenhagen-Roberts noncommutative space-time
• Algebraic Structure of Dirac Hamiltonians in Non-Commutative Phase Space
• Dynamics of semiclassical Bloch wave - packets
• The standard electroweak model in the noncommutative $DFR$ space-time
• Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets
• Exotic Newton-Hooke group, noncommutative plane and superconformal symmetry
• Relativistic particle dynamics in D=2+1
• Electromagnetic Excitations of Hall Systems on Four Dimensional Space
• N=2 supersymmetric radiation damping problem on a noncommutative plane