Noncommutative Quantum Mechanics and Seiberg-Witten Map

Abstract

In order to overcome ambiguity problem on identification of mathematical objects in noncommutative theory with physical observables, quantum mechanical system coupled to the NC U(1) gauge field in the noncommutative space is reformulated by making use of the unitarized Seiberg-Witten map, and applied to the Aharonov-Bohm and Hall effects of the NC U(1) gauge field. Retaining terms only up to linear order in the NC parameter θ, we find that the AB topological phase and the Hall conductivity have both the same formulas as those of the ordinary commutative space with no θ-dependence.

7 pages, no figures, uses revtex4; 8 pages, conclusion changed, Appendix added

References in corpus (27)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Noncommutative Perturbative Dynamics
• Noncommutative Field Theory and Lorentz Violation
• D-branes and Deformation Quantization
• Non-Commutative Quantum Mechanics
• The IR/UV Connection in the Non-Commutative Gauge Theories
• Quantum mechanics on the noncommutative plane and sphere
• Magnetic fields, branes and noncommutative geometry
• Perturbative analysis on infrared aspects of noncommutative QED on R^4
• The exotic Galilei group and the "Peierls substitution"
• Features of Time-independent Wigner Functions
• Exotic galilean symmetry in the non-commutative plane, and the Hall effect
• Low-energy Limits on the Antisymmetric Tensor Field Background on the Brane and on the Non-commutative Scale
• Signals for Non-Commutative Interactions at Linear Colliders
• Perturbative analysis on infrared and ultraviolet aspects of noncommutative QED on R^4
• Aharonov-Bohm Effect in Noncommutative Spaces
• Bounding Noncommutative QCD
• Comments on Non-Commutative Phenomenology
• Quantum Theories on Noncommutative Spaces with Nontrivial Topology: Aharonov-Bohm and Casimir Effects
• Hall Effect in Noncommutative Coordinates
• Testing spatial noncommutativiy via the Aharonov-Bohm effect
• Supersymmetric Noncommutative QED and Lorentz Violation
• Perturbative Analysis of the Seiberg-Witten Map
• Hall Effect on Noncommutative Phase Space
• Hall effect in Noncommutative spaces

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• Dual families of non-commutative quantum systems
• A comparative review of four formulations of noncommutative quantum mechanics
• The Aharonov-Bohm Effect in Noncommutative Quantum Mechanics
• Seiberg-Witten map and Galilean symmetry violation in a non-commutative planar system
• Magnetic fields in noncommutative quantum mechanics
• Noncommutative Quantum Hall Effect and Aharonov-Bohm Effect
• Energy-dependent noncommutative quantum mechanics
• Tensor Operators in Noncommutative Quantum Mechanics
• Lamb shift and Stark effect in simultaneous space-space and momentum-momentum noncommutative quantum mechanics and $\theta$-deformed $su(2)$ algebra
• Dynamical symmetries in noncommutative theories
• Noncommutative relativistic particles
• U(1) gauge invariant noncommutative Schrödinger theory and gravity
• Angular momentum quantum backflow in the noncommutative plane
• An Introduction to Noncommutative Physics
• Free-fall in a uniform gravitational field in non-commutative quantum mechanics
• Self-quartic interaction for a scalar field in an extended DFR noncommutative spacetime
• Noncommutativity in (2+1)-dimensions and the Lorentz group
• Noncommutative Particles in Curved Spaces
• Lowest Landau level theory of the bosonic Jain states
• Some aspects of quantum mechanics and field theory in a Lorentz invariant noncommutative space
• Klein-Gordon theory in noncommutative phase space
• The Noncommutative Harmonic Oscillator based in Simplectic Representation of Galilei Group
• The Noncommutative Doplicher-Fredenhagen-Roberts-Amorim Space
• On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
• Complete noncommutativity in a cosmological model with radiation
• Quantum and pseudoclassical descriptions of nonrelativistic spinning particles in noncommutative space
• Quantum and pseudoclassical descriptions of nonrelativistic spinning particles in noncommutative space
• Canonical Structure of Noncommutative Quantum Mechanics as Constraint System
• The Strong Interaction Model in DFR noncommutative space-time
• Big Bang Nucleosynthesis constraints on space-time noncommutativity
• A general relativity formulation for the Doplicher-Fredenhagen-Roberts noncommutative space-time
• Causality in noncommutative spacetime
• The standard electroweak model in the noncommutative $DFR$ space-time