Noncommutative Geometry and Geometric Phases

Abstract

We have studied particle motion in generalized forms of noncommutative phase space, that simulate monopole and other forms of Berry curvature, that can be identified as effective internal magnetic fields, in coordinate and momentum space. The Ahranov-Bohm effect has been considered in this form of phase space, with operatorial structures of noncommutativity. Physical significance of our results are also discussed.

Revised version, Reference added, to appear in Euro.Phys.Lett

References in corpus (28)

• String Theory and Noncommutative Geometry
• Quantum Field Theory on Noncommutative Spaces
• Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
• Anomalous Hall Effect and Magnetic Monopoles in Momentum-Space
• Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
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• Classical and Quantum Mechanics of Free \k Relativistic Systems
• Quantum mechanics on the noncommutative plane and sphere
• Topological Nature of Anomalous Hall Effect in Ferromagnet
• The exotic Galilei group and the "Peierls substitution"
• Features of Time-independent Wigner Functions
• Chirality driven anomalous Hall effect in weak coupling regime
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• Transverse Spin-Orbit Force in the Spin Hall Effect in Ballistic Semiconductor Wires
• Quantum Mechanics on a Noncommutative Brane in M(atrix) Theory
• $\kappa$-Minkowski Spacetime Through Exotic "Oscillator"
• Field theory on kappa-spacetime
• The $AdS$ particle
• A Novel "Magnetic" Field And Its Dual Non-Commutative Phase Space
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• Lie Particle And Its Batalin-Tyutin Extension

Cited by in corpus (10)

• The Noncommutative Anandan's Quantum Phase
• Noncommutative Quantum Hall Effect and Aharonov-Bohm Effect
• Landau Analog Levels for Dipoles in the Noncommutative Space and Phase Space
• Exotic galilean symmetry and non-commutative mechanics
• Inertial spin Hall effect in noncommutative space
• Scattering of spin 1/2 particles by the 2+1 dimensional noncommutative Aharonov-Bohm potential
• A Novel "Magnetic" Field And Its Dual Non-Commutative Phase Space
• On atomic analogue of Landau quantization
• From Feynman Proof of Maxwell Equations to Noncommutative Quantum Mechanics
• Quantum dot with spin-orbit interaction in noncommutative phase space and analog Landau levels