The Newton–Nelson equation on fiber bundles with connections
Yu. E. Gliklikha, N. V. Vinokurovab
a Voronezh State University
b Kursk State University
The paper is a survey with modifications on the research of the so-called Newton–Nelson equation (the equation of motion in Nelson's stochastic mechanics) on the total space of a bundle in two cases: where the base of the bundle is a Riemannian manifold and the bundle is real and where the base of the bundle is a Lorentz manifold and the bundle is complex. In the latter case, we describe the relations with the equation of motion of the quantum particle in the classical gauge field (the above-mentioned connection). Besides, a certain second-order ordinary differential equation on the bundle with connection that is interpreted as the equation of motion of the classical particle in the classical gauge field is described.
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Journal of Mathematical Sciences (New York), 2017, 225:4, 575–589
Yu. E. Gliklikh, N. V. Vinokurova, “The Newton–Nelson equation on fiber bundles with connections”, Fundam. Prikl. Mat., 20:3 (2015), 61–81; J. Math. Sci., 225:4 (2017), 575–589
Citation in format AMSBIB
\by Yu.~E.~Gliklikh, N.~V.~Vinokurova
\paper The Newton--Nelson equation on fiber bundles with connections
\jour Fundam. Prikl. Mat.
\jour J. Math. Sci.
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