Abstract
It is shown that the classical equations of motion for particles having internal degrees of freedom, i.e., spin (Nyborg equations) allow for a geometrization on a special manifold V4. It is also shown that the equation for a harmonic function on V4 (with an additional vector bundle on which a spinor connection is defined) is a squared Dirac equation.
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K. B. Korotchenko, Izv. Vyssh. Uchebn. Zaved. Fiz., No. 9, 70 (1990).
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B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Modern Geometry: Methods and Applications [in Russian], Nauka, Moscow (1979).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 76–80, October, 1990.
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Korotchenko, K.B. Simultaneous geometrization of classical and quantum mechanics of particles with spin. Soviet Physics Journal 33, 875–879 (1990). https://doi.org/10.1007/BF00897313
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DOI: https://doi.org/10.1007/BF00897313