Noncommutative Planar Particle Dynamics with Gauge Interactions

Abstract

We consider two ways of introducing minimal Abelian gauge interactions into the model presented in [1]. They are different only if the second central charge of the planar Galilei group is nonzero. One way leads to standard gauge transformations and second to a generalized gauge theory with gauge transformations accompanied by time-dependent area-preserving coordinate transformations. Both approaches, however, are related to each other by a classical Seiberg-Witten map supplemented by the noncanonical transformation of the phase space variables for planar particles. We also formulate the two-body problem in the model with a generalized gauge symmetry and consider the case with both CS and background electromagnetic fields, as it is used in the description of fractional quantum Hall effect.

24 pages - version to be published in Annals of Physics

References in corpus (8)

• The quantum structure of spacetime at the Planck scale and quantum fields
• Noncommutative Quantum Mechanics from Noncommutative Quantum Field Theory
• Exotic galilean symmetry in the non-commutative plane, and the Hall effect
• Non-relativistic anyons, exotic Galilean symmetry and noncommutative plane
• Covariant Coordinate Transformations on Noncommutative Space
• Second central extension in Galilean covariant field theory
• Particle-vortex dynamics in noncommutative space
• Deformed Chern-Simons interaction for nonrelativistic point particles

Cited by in corpus (24)

• Noncommutative General Relativity
• Position-dependent noncommutativity in quantum mechanics
• Nonrelativistic anyons in external electromagnetic field
• Chiral fermions as classical massless spinning particles
• Poincare covariant mechanics on noncommutative space
• Exotic galilean symmetry and non-commutative mechanics
• Doubly Special Relativity in Position Space Starting from the Conformal Group
• On the Landau system in noncommutative phase-space
• A New Type of Conformal Dynamics
• Anyons, group theory and planar physics
• Non-commutative oscillator with Kepler-type dynamical symmetry
• Dirac Quantization Condition for Monopole in Noncommutative Space-Time
• Relativistic Spinning Particle in a Non-Commutative Extended Spacetime
• Fingerprints of the quantum space-time in time-dependent quantum mechanics: An emergent geometric phase
• On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
• Noncommutative quantum mechanics of simple matter systems interacting with circularly polarized gravitational waves
• N=2 Supersymmetric Planar Particles and Magnetic Interaction from Noncommutativity
• Comments on spin-orbit interaction of anyons
• Path integral action and Chern-Simons quantum mechanics in noncommutative plane
• The E(2) Particle
• Gauge invariance and classical dynamics of noncommutative particle theory
• From Noncommutative Sphere to Nonrelativistic Spin
• Path-integral action of a particle in the noncommutative phase-space
• Space-time Schrödinger symmetries of a post-Galilean particle