Abstract
We shortly describe classical models of spinning electron and list a number of theoretical issues where these models turn out to be useful. Then we discuss the possibility to extend the range of applicability of these models by introducing an interaction,that forces the spin to align up or down relative to its precession axis.
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Notes
Consider either frozen particle in constant magnetic field, or on circular trajectory in the Coulomb electric and constant magnetic fields.
The construction can be resumed as follows: variational problem with the Lagrangian \(L = {{\dot {x}}^{2}} + \mathop {\dot {\omega }}\nolimits^2 - \sqrt {{{{({{{\dot {x}}}^{2}} + {{{\dot {\omega }}}^{2}})}}^{2}} - 4{{{(\dot {x}\dot {\omega })}}^{2}}} \) implies the constraint \(({\mathbf{p}},\pi ) \equiv \left( {\tfrac{{\partial L}}{{\partial {\mathbf{\dot {x}}}}},\tfrac{{\partial L}}{{\partial \dot {\omega }}}} \right) = 0\) as one of the extreme conditions.
In the language of Poisson geometry this equation means that \({{S}^{{\mu \nu }}}{{p}_{\nu }}\) are Casimir functions of the Poisson structure.
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FUNDING
The work of A. A. D. has been supported by the Brazilian foundation CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico—Brasil), and by Tomsk State University Competitiveness Improvement Program.
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Deriglazov, A.A. Nonminimal Spin-Field Interaction of the Classical Electron and Quantization of Spin. Phys. Part. Nuclei Lett. 17, 738–743 (2020). https://doi.org/10.1134/S1547477120050131
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DOI: https://doi.org/10.1134/S1547477120050131