Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-02-22
Phys.Rev.D81:085024,2010
Physics
High Energy Physics
High Energy Physics - Theory
11 pages, references addad
Scientific paper
10.1103/PhysRevD.81.085024
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, $\Delta x\Delta y\geq\theta^{2}/2$, 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.
da Silva Adilson Jose
Gomes Marcelo
Kupriyanov V. G.
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