Magnetic fields in noncommutative quantum mechanics

Abstract

We discuss various descriptions of a quantum particle on noncommutative space in a (possibly non-constant) magnetic field. We have tried to present the basic facts in a unified and synthetic manner, and to clarify the relationship between various approaches and results that are scattered in the literature.

Dedicated to the memory of Julius Wess. Work presented by F. Gieres at the conference `Non-commutative Geometry and Physics' (Orsay, April 2007)

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Cited by in corpus (38)

• Magnetic-Dipole Spin Effects in Noncommutative Quantum Mechanics
• PT-symmetric noncommutative spaces with minimal volume uncertainty relations
• Strings from position-dependent noncommutativity
• Exotic galilean symmetry and non-commutative mechanics
• Aharonov-Bohm effect in a Class of Noncommutative Theories
• Noncommutative quantum mechanics -- a perspective on structure and spatial extent
• A Deformation Quantization Theory for Non-Commutative Quantum Mechanics
• Non-commutativity and non-inertial effects on a scalar field in a cosmic string space-time. Part 2: Spin-zero Duffin-Kemmer-Petiau-like oscillator
• Detecting Noncommutative Phase Space by Aharonov-Bohm Effect
• Non-commutative Supersymmetric Quantum Mechanics
• Semiclassical and quantum description of motion on noncommutative plane
• An Introduction to Noncommutative Physics
• On the Fisk-Tait Equation for Spin-3/2 Fermions Interacting With an External Magnetic Field in Noncommutative Space-Time
• Non-commutativity and non-inertial effects on a scalar field in a cosmic string space-time. Part 1: Klein-Gordon oscillator
• Analytical Solution of (2+1) Dimensional Dirac Equation in Time-Dependent Noncommutative Phase-Space
• Lowest Landau level theory of the bosonic Jain states
• Klein-Gordon theory in noncommutative phase space
• Position-dependent mass in strong quantum gravitational background fields
• On the Plethora of Representations Arising in Noncommutative Quantum Mechanics and An Explicit Construction of Noncommutative 4-tori
• Wigner Functions for Noncommutative Quantum Mechanics: a group representation based construction
• Triply Extended Group of Translations of ${\mathbb{R}}^4$ as Defining Group of NCQM: relation to various gauges
• Wong's Equations and Charged Relativistic Particles in Non-Commutative Space
• Quantum and pseudoclassical descriptions of nonrelativistic spinning particles in noncommutative space
• Quantum and pseudoclassical descriptions of nonrelativistic spinning particles in noncommutative space
• Aspects of perturbative quantum field theory on non-commutative spaces
• Gauge invariant energy spectra in 2-dimensional noncommutative quantum mechanics
• On a charged spinless point particle minimally coupled to a constant magnetic field in a noncommutative plane
• Quantum dot with spin-orbit interaction in noncommutative phase space and analog Landau levels
• Comments on noncommutative quantum mechanical systems associated with Lie algebras
• Field Theory with Coordinate Dependent Noncommutativity
• Quantum simulation of quantum mechanical system with spatial noncommutativity
• Big Bang Nucleosynthesis constraints on space-time noncommutativity
• Uncertainty relations for a non-canonical phase-space noncommutative algebra
• Dynamics determines geometry
• Noncommutative coherent states and related aspects of Berezin-Toeplitz quantization
• New parameters of Non-commutativity in Quantum Mechanics
• Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets
• Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space