Noncommutativity due to spin

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.Comment: 11 pages, references adda

Limits on dark matter proton scattering from neutrino telescopes using micrOMEGAs

Limits on dark matter spin dependent elastic scattering cross section on protons derived from IceCube data are obtained for different dark matter annihilation channels using micrOMEGAs. The uncertainty on the derived limits, estimated by using different neutrino spectra, can reach a factor two. For all dark matter annihilation channels except for quarks, the limits on the spin dependent cross section are more stringent than those obtained in direct detection experiments. The new functions that allow to derive those limits are described.Comment: 23 pages, 7 figures; v2: references added; v3 and v4: clarifications added; The code can be downloaded from https://lapth.cnrs.fr/micromega

Revisão da metodologia analítica de determinação do extrato seco de vinho.

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Ação de regulador do metabolismo de etileno sobre a produtividade de soja cultivada em terras baixas.

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Camalhões de base larga: uma opção para drenagem superficial de várzeas muito planas na região costeira do Rio Grande do Sul.

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