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

References in corpus (11)

• Position-dependent noncommutativity in quantum mechanics
• Magnetic-Dipole Spin Effects in Noncommutative Quantum Mechanics
• Star products made (somewhat) easier
• Canonical quantization of so-called non-Lagrangian systems
• Wigner Oscillators, Twisted Hopf Algebras and Second Quantization
• Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action
• Scattering of spin 1/2 particles by the 2+1 dimensional noncommutative Aharonov-Bohm potential
• Noncommutative quantum mechanics as a gauge theory
• Born series and unitarity in noncommutative quantum mechanics
• Nilpotent noncommutativity and renormalization
• Space-time noncommutativity with a bifermionic parameter

Cited by in corpus (1)

• Twist Deformation of Rotationally Invariant Quantum Mechanics