Dynamics of a Dirac Fermion in the presence of spin noncommutativity

Abstract

Recently, it has been proposed a spacetime noncommutativity that involves spin degrees of freedom, here called "spin noncommutativity". One of the motivations for such a construction is that it preserves Lorentz invariance, which is deformed or simply broken in other approaches to spacetime noncommutativity. In this work, we gain further insight in the physical aspects of the spin noncommutativity. The noncommutative Dirac equation is derived from an action principle, and it is found to lead to the conservation of a modified current, which involves the background electromagnetic field. Finally, we study the Landau problem in the presence of spin noncommutativity. For this scenario of a constant magnetic field, we are able to derive a simple Hermitean non-commutative correction to the Hamiltonian operator, and show that the degeneracy of the excited states is lifted by the noncommutativity at the second order or perturbation theory.

18 pages, revtex4

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• Noncommutative Spaces and Poincaré Symmetry
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• Hydrogen atom in rotationally invariant noncommutative space
• Noncommutative phase space with rotational symmetry and hydrogen atom
• Rotationally invariant noncommutative phase space of canonical type with recovered weak equivalence principle
• Klein-Gordon theory in noncommutative phase space
• Classical electrodynamics in a space with spin noncommutativity of coordinates
• System of interacting harmonic oscillators in rotationally invariant noncommutative phase space
• Time reversal and rotational symmetries in noncommutative phase space
• Effects of wave propagation in canonical Poisson gauge theory under an external magnetic field
• Variational problem for Hamiltonian system on so(k, m) Lie-Poisson manifold and dynamics of semiclassical spin
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Minimal momentum estimation in noncommutative phase space of canonical type with preserved rotational and time reversal symmetries
• Twisted Supersymmetry in a Deformed Wess-Zumino Model in (2+1) Dimensions
• Chiral Spin Noncommutative Space and Anomalous Dipole Moments
• Harmonic oscillator chain in noncommutative phase space with rotational symmetry