Noncommutative Point Sources

Abstract

We construct a perturbative solution to classical noncommutative gauge theory on ${\mathbb{R}}^3$ minus the origin using the Groenewald-Moyal star product. The result describes a noncommutative point charge. Applying it to the quantum mechanics of the noncommutative hydrogen atom gives shifts in the $1S$ hyperfine splitting which are first order in the noncommutativity parameter.

8 pages

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• Particle-like solutions to classical noncommutative gauge theory
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• Effect of coordinate noncommutativity on the mass of a particle in a uniform field and the equivalence principle
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• Bounds on the Parameter of Noncommutativity from Supernova SN1987A
• Effect of noncommutativity on the spectrum of free particle and harmonic oscillator in rotationally invariant noncommutative phase space
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• Response of simple quantum systems to different polarizations of gravitational waves in noncommutative phase-space
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• Kinematic variables in noncommutative phase space and parameters of noncommutativity
• Resonant-bar detectors of gravitational wave as possible probe of the noncommutative structure of space
• A New Limit for the Non-Commutative Space-Time Parameter
• Nonlinear corrections in basic problems of electro- and magneto-statics in the vacuum
• Galilean symmetry in noncommutative Gravitational Quantum Well
• Two-dimensional pauli equation in noncommutative phase-space
• Footprint of spatial noncommutativity in resonant detectors of gravitational wave
• Noncommutative phase space with rotational symmetry and hydrogen atom
• Perturbation of the ns energy levels of the hydrogen atom in rotationally invariant noncommutative space
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• Classical electrodynamics in a space with spin noncommutativity of coordinates
• Constraining GUP Models Using Limits on SME Coefficients
• Wong's Equations and Charged Relativistic Particles in Non-Commutative Space
• Noncommutative magnetic moment, fundamental length and lepton size
• Signatures of noncommutativity in bar detectors of gravitational waves
• Equivalence principle in context of large uniform acceleration - a quantum mechanical perspective
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• Two-particle system in noncommutative space with preserved rotational symmetry
• Noncommutative quantum mechanics of simple matter systems interacting with circularly polarized gravitational waves
• When electric charge becomes also magnetic
• Noncommutative black hole in the Finslerian spacetime
• Noncommutative of space-time and the relativistic Hydrogen atom
• Neutrino-electron scattering in noncommutative space
• Noncommutative QED+QCD and $\beta$-function for QED
• Particle Classification and Dynamics in GL(2,C) Gravity
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• Influence of noncommutativity on the motion of Sun-Earth-Moon system and the weak equivalence principle
• Remarks on an Exact Seiberg-Witten map
• Thermodynamical features of Verlinde's approach for a non-commutative Schwarzschild-anti-deSitter black hole in a broad range of scales
• Quasinormal modes of noncommutative geometry-inspired dirty black holes
• Emergent Abelian Gauge Fields from Noncommutative Gravity
• Trace of phase-space noncommutativity in the response of a free particle to linearized gravitational waves
• Quantum mechanics of a charged particle in a background magnetic field interacting with linearized gravitational waves
• Interaction of a circularly polarised gravitational wave with a charged particle in a static magnetic background