Noncommutativity due to spin

Abstract

Using the Berezin-Marinov pseudoclassical formulation of spin particle we propose a classical model of spin noncommutativity. In the nonrelativistic case, the Poisson brackets between the coordinates are proportional to the spin angular momentum. The quantization of the model leads to the noncommutativity with mixed spacial and spin degrees of freedom. A modified Pauli equation, describing a spin half particle in an external e.m. field is obtained. We show that nonlocality caused by the spin noncommutativity depends on the spin of the particle; for spin zero, nonlocality does not appear, for spin half, $\Delta x\Delta y\ge {\theta }^2/2$, etc. In the relativistic case the noncommutative Dirac equation was derived. For that we introduce a new star product. The advantage of our model is that in spite of the presence of noncommutativity and nonlocality, it is Lorentz invariant. Also, in the quasiclassical approximation it gives noncommutativity with a nilpotent parameter.

11 pages, references addad

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• Noncommutative Spaces and Poincaré Symmetry
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• Aharonov-Bohm effect in a Class of Noncommutative Theories
• Relativistic corrections to the algebra of position variables and spin-orbital interaction
• Quantum mechanics with coordinate dependent noncommutativity
• Dynamics of a Dirac Fermion in the presence of spin noncommutativity
• Noncommutative Space Corrections on the Klein-Gordon and Dirac Oscillators Spectra
• Chern-Simons terms in Lifshitz like quantum electrodynamics
• Twist Deformation of Rotationally Invariant Quantum Mechanics
• Noncommutative phase space with rotational symmetry and hydrogen atom
• Noncommutativity in (2+1)-dimensions and the Lorentz group
• Dirac equation on coordinate dependent noncommutative space-time
• Klein-Gordon theory in noncommutative phase space
• Spin Non-commutativity and the Three-Dimensional Harmonic Oscillator
• Classical electrodynamics in a space with spin noncommutativity of coordinates
• Magnetic Monopoles in (Noncommutative) Quantum Mechanics
• Dirac equation, hydrogen atom spectrum and the Lamb shift in dynamical noncommutative spaces
• Deformed classical-quantum mechanics transition
• Conserved symmetries in noncommutative quantum mechanics
• Microcausality of spin-induced noncommutative theories
• Testing Spatial Noncommutativity via Magnetic Hyperfine Structure Induced by Fractional Angular Momentum of Rydberg System
• The 1/N Expansion in Noncommutative Quantum Mechanics
• Vacuum Pair Creation in Spin Noncommutative of Coordinates: Volkov Background and Constant Electric Field