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

References in corpus (32)

• Hydrogen Atom Spectrum and the Lamb Shift in Noncommutative QED
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• Non-Commutative Quantum Mechanics
• Quantum mechanics on the noncommutative plane and sphere
• The exotic Galilei group and the "Peierls substitution"
• UV divergence-free QFT on noncommutative plane
• Galilean-Invariant (2+1)-Dimensional Models with a Chern-Simons-Like Term and D=2 N oncommutative Geometry
• Spin and Statistics on the Groenewold-Moyal Plane: Pauli-Forbidden Levels and Transitions
• Twisted Statistics in kappa-Minkowski Spacetime
• Classical and quantum mechanics of the nonrelativistic Snyder model
• Minimal length in Quantum Mechanics and non-Hermitian Hamiltonian systems
• On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• Noncommutative Gauge Theory without Lorentz Violation
• Dirac Equation in Noncommutative Space for Hydrogen Atom
• Position-dependent noncommutativity in quantum mechanics
• Deformed Symmetry in Snyder Space and Relativistic Particle Dynamics
• Poincare covariant mechanics on noncommutative space
• Noncommutative relativistic particle on the electromagnetic background
• Magnetic-Dipole Spin Effects in Noncommutative Quantum Mechanics
• Twist to close
• Snyder space revisited
• Noncommutativity due to spin
• Particle Dynamics on Snyder space
• Quantum mechanics on noncommutative plane and sphere from constrained systems
• On Ward Identities in Lifshitz-like Field Theories
• Wigner Oscillators, Twisted Hopf Algebras and Second Quantization
• Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action
• Classical Noncommutative Electrodynamics with External Source
• Scattering of spin 1/2 particles by the 2+1 dimensional noncommutative Aharonov-Bohm potential
• The three-dimensional noncommutative Gross-Neveu model
• The 1/N Expansion in Noncommutative Quantum Mechanics

Cited by in corpus (19)

• Hydrogen atom on curved noncommutative space
• Noncommutative Spaces and Poincaré Symmetry
• Lagrangian for Frenkel electron and position's non-commutativity due to spin
• Energy-dependent noncommutative quantum mechanics
• Relativistic corrections to the algebra of position variables and spin-orbital interaction
• 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