A Novel "Magnetic" Field And Its Dual Non-Commutative Phase Space

Abstract

In this paper we have studied a new form of Non-Commutative (NC) phase space with an operatorial form of noncommutativity. A point particle in this space feels the effect of an interaction with an "{\it{internal}}" magnetic field, that is singular at a specific position ${\theta }^{-1}$. By "internal" we mean that the effective magnetic fields depends essentially on the particle properties and modifies the symplectic structure. Here $\theta$ is the NC parameter and induces the coupling between the particle and the "internal" magnetic field. The magnetic moment of the particle is computed. Interaction with an {\it{external}} physical magnetic field reveals interesting features induced by the inherent fuzziness of the NC phase space: introduction of non-trivial structures into the charge and mass of the particle and possibility of the particle dynamics collapsing to a Hall type of motion. The dynamics is studied both from Lagrangian and symplectic (Hamiltonian) points of view. The canonical (Darboux) variables are also identified. We briefly comment, that the model presented here, can play interesting role in the context of (recently observed) {\it{real}} space Berry curvature in material systems.

8 pages LaTex, Matches journal version, PLB 638 (2006)350; One reference added and minor change in text, related to it

References in corpus (8)

• Berry phase correction to electron density of states in solids
• Anomalous Hall Effect and Skyrmion Number in Real- and Momentum-space
• Berry phase correction to electron density in solids and "exotic" dynamics
• $\kappa$-Minkowski Spacetime Through Exotic "Oscillator"
• Comment on "Berry phase correction to electron density in solids" by Xiao et al
• The $AdS$ particle
• Noncommutative Geometry and Geometric Phases
• Hamiltonian aspects of Bogoliubov quasiparticles

Cited by in corpus (5)

• Semiclassical Diagonalization of Quantum Hamiltonian and Equations of Motion with Berry Phase Corrections
• Exotic galilean symmetry and non-commutative mechanics
• Noncommutative Geometry and Geometric Phases
• Study of the "Non-Abelian" Current Algebra of a Non-linear $\sigma$-Model
• (1+1) Newton-Hooke Group for the Simple and Damped Harmonic Oscillator