Exotic galilean symmetry in the non-commutative plane, and the Hall effect

Abstract

Quantum Mechanics in the non-commutative plane is shown to admit the ``exotic'' symmetry of the doubly-centrally-extended Galilei group. When coupled to a planar magnetic field whose strength is the inverse of the non-commutative parameter, the system becomes singular, and ``Faddeev-Jackiw'' reduction yields the ``Chern-Simons'' mechanics of Dunne, Jackiw, and Trugenberger. The reduced system moves according to the Hall law.

Revised version. The formula for the conserved quantities is corrected; some more references added. 11 pages, LaTex, no figures

References in corpus (1)

• Testing Non-commutative QED, Constructing Non-commutative MHD

Cited by in corpus (138)

• Non-relativistic conformal symmetries and Newton-Cartan structures
• The non-commutative Landau problem
• Spin Hall effect and Berry phase of spinning particles
• Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces
• Testing spatial noncommutativiy via the Aharonov-Bohm effect
• Weyl-Wigner Formulation of Noncommutative Quantum Mechanics
• Anyon wave equations and the noncommutative plane
• Spectrum of Schroedinger field in a noncommutative magnetic monopole
• Dual families of non-commutative quantum systems
• Scaling of variables and the relation between noncommutative parameters in Noncommutative Quantum Mechanics
• Acceleration-Extended Galilean Symmetries with Central Charges and their Dynamical Realizations
• (2+1)D Exotic Newton-Hooke Symmetry, Duality and Projective Phase
• A comparative review of four formulations of noncommutative quantum mechanics
• Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry
• Non-relativistic anyons, exotic Galilean symmetry and noncommutative plane
• Aspects of Phase-Space Noncommutative Quantum Mechanics
• Seiberg-Witten map and Galilean symmetry violation in a non-commutative planar system
• Interactions and non-commutativity in quantum Hall systems
• Composite system in noncommutative space and the equivalence principle
• Position-dependent noncommutativity in quantum mechanics
• Phase-Space Noncommutativity and the Dirac Equation
• Monopole and Berry Phase in Momentum Space in Noncommutative Quantum Mechanics
• Quantum Theory of Noncommutative Fields
• Berry Phase in the Gravitational Quantum Well and the Seiberg-Witten map
• (Super)Oscillator on CP(N) and Constant Magnetic Field
• Nonrelativistic anyons in external electromagnetic field
• Chiral fermions as classical massless spinning particles
• Magnetic fields in noncommutative quantum mechanics
• Phases in noncommutative quantum mechanics on (pseudo)sphere
• Noncommutative Quantum Mechanics and Seiberg-Witten Map
• Bosons, fermions and anyons in the plane, and supersymmetry
• Noncommutative Dirac oscillator in an external magnetic field
• Noncommutative relativistic particle on the electromagnetic background
• Thermodynamical properties of graphene in noncommutative phase-space
• Planar Carrollean dynamics, and the Carroll quantum equation
• Probing phase-space noncommutativity through quantum beating, missing information and the thermodynamic limit
• Noncommutativity due to spin
• Gauge Covariance of the Aharonov-Bohm Phase in Noncommutative Quantum Mechanics
• A note on the Chevalley-Eilenberg Cohomology for the Galilei and Poincare Algebras
• Harmonic oscillator in a background magnetic field in noncommutative quantum phase-space
• Wigner Measures in Noncommutative Quantum Mechanics
• Spin and exotic Galilean symmetry
• Exotic galilean symmetry and non-commutative mechanics
• Non-relativistic symmetries in three space-time dimensions and the Nappi-Witten algebra
• Anyons with anomalous gyromagnetic ratio & the Hall effect
• Noncommutative Planar Particle Dynamics with Gauge Interactions
• Exact solution of two dimensional Dunkl harmonic oscillator in Non-Commutative phase-space
• Space-Time Noncommutativity from Particle Mechanics
• Aharonov-Casher effect for spin one particles in a noncommutative space
• Enlarged Galilean symmetry of anyons and the Hall effect
• On the Landau system in noncommutative phase-space
• On the Hamiltonian nature of semiclassical equations of motion in the presence of an electromagnetic field and Berry curvature
• A Noncommutative Space Approach to Confined Dirac Fermions in Graphene
• Classical dynamics on curved Snyder space
• Lagrangian formulation for noncommutative nonlinear systems
• NC Branes and Hierarchies in Quantum Hall Fluids
• A Deformation Quantization Theory for Non-Commutative Quantum Mechanics
• Electric Chern-Simons term, enlarged exotic Galilei symmetry and noncommutative plane
• Super-extended noncommutative Landau problem and conformal symmetry
• Exact master equation for a noncommutative Brownian particle
• A New Type of Conformal Dynamics
• Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action
• Anyons, group theory and planar physics
• Non-commutative Supersymmetric Quantum Mechanics
• Non-commutative oscillator with Kepler-type dynamical symmetry
• U(1) gauge invariant noncommutative Schrödinger theory and gravity
• Angular momentum quantum backflow in the noncommutative plane
• Semiclassical and quantum description of motion on noncommutative plane
• Constant magnetic field and 2d non-commutative inverted oscillator
• Kohn condition and exotic Newton-Hooke symmetry in the non-commutative Landau problem
• Dynamical noncommutativity
• Resonant-bar detectors of gravitational wave as possible probe of the noncommutative structure of space
• Bosonized supersymmetry of anyons and supersymmetric exotic particle on the non-commutative plane
• Chiral bosonization for non-commutative fields
• Footprint of spatial noncommutativity in resonant detectors of gravitational wave
• Twist Deformation of Rotationally Invariant Quantum Mechanics
• Relativistic Spinning Particle in a Non-Commutative Extended Spacetime
• Group theoretical construction of planar Noncommutative Phase Spaces
• Thermodynamics of a charged particle in a noncommutative plane in a background magnetic field
• Noncommutative quantum mechanics as a gauge theory
• A (p,q)-deformed Landau problem in a spherical harmonic well: spectrum and noncommuting coordinates
• Path-integral quantization of Galilean Fermi fields
• Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras
• Wong's Equations and Charged Relativistic Particles in Non-Commutative Space
• Effects of Twisted Noncommutativity in Multi-particle Hamiltonians
• On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
• Fate of the Superconducting Ground State on the Moyal Plane
• Emergent entropy of exotic oscillators and squeezing in three-wave mixing process
• Non-Commutativity effects in the Dirac equation in crossed electric and magnetic fields
• Analytical and numerical analysis of a rotational invariant D=2 harmonic oscillator in the light of different noncommutative phase-space configurations
• Exotic Hill Problem: Hall motions and symmetries
• Noncommutative Phase Spaces by Coadjoint Orbits Method
• Noncommutative Fluids
• Physical Observables for Noncommutative Landau Levels
• Noncommutative quantum mechanics of simple matter systems interacting with circularly polarized gravitational waves
• Extended Space Duality in the Noncommutative Plane
• From Feynman Proof of Maxwell Equations to Noncommutative Quantum Mechanics
• N=2 Supersymmetric Planar Particles and Magnetic Interaction from Noncommutativity
• Path integral action of a particle in a magnetic field in the noncommutative plane and the Aharonov-Bohm effect
• A note on broken dilatation symmetry in planar noncommutative theory
• Landau levels in a 2D noncommutative space: matrix and quaternionic vector coherent states
• Supersymmetry in the Non-Commutative Plane
• Path integral action and Chern-Simons quantum mechanics in noncommutative plane
• Dynamical sectors for a spinning particle in AdS_3
• Quantum Theory of Tensionless Noncommutative p-Branes
• Various disguises of the Pais-Uhlenbeck oscillator
• Weak-strong duality of the non-commutative Landau problem induced by a two-vortex permutation, and conformal bridge transformation
• Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane
• Localization at threshold in noncommutative space
• Transverse Shifts in Paraxial Spinoptics
• Deformed Chern-Simons interaction for nonrelativistic point particles
• On a charged spinless point particle minimally coupled to a constant magnetic field in a noncommutative plane
• Gauge invariance and classical dynamics of noncommutative particle theory
• Collapsing Shells and Black Holes: a quantum analysis
• Fate of $\kappa$-Minkowski space-time in non-relativistic (Galilean) and ultra-relativistic (Carrollian) regimes
• Quantum dot with spin-orbit interaction in noncommutative phase space and analog Landau levels
• Exotic Non-relativistic String
• Galilei Group with multiple central extension, vorticity and entropy generation: "Exotic" fluid in 3+1-dimensions
• Path-integral action of a particle in the noncommutative phase-space
• Noncommutative Phase Spaces on Aristotle group
• Dirac equation with a magnetic field in 3D non-commutative phase space
• Group Theoretical Construction of Planar Noncommutative Systems
• (1+1) Newton-Hooke Group for the Simple and Damped Harmonic Oscillator
• Uncertainty relations for a non-canonical phase-space noncommutative algebra
• Inverse square problem and so(2,1) symmetry in noncommutative space
• Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets
• Perturbed nonlinear models from Noncommutativity
• Emergent spacetime from a Berry-inspired dynamical gauge field coupled to electromagnetism
• Algebraic Structure of Dirac Hamiltonians in Non-Commutative Phase Space
• Study on Noncommutative Representations of Galilean Generators
• Exotic Newton-Hooke group, noncommutative plane and superconformal symmetry
• Theories on noncommutative spaces and deformed symmetries
• Electromagnetic Excitations of Hall Systems on Four Dimensional Space
• Noncommutative Classical Dynamics on Velocity Phase Space and Souriau Formalism
• Statistical interparticle potential on noncommutative space
• On the magnetic 2+1- D space-time and its non-relativistic counterpart
• N=2 supersymmetric radiation damping problem on a noncommutative plane
• Noncommutative scalar fields from symplectic deformation