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On the description of motion of a quantum particle in the classical gauge field in the language of stochastic mechanics. (English) Zbl 1315.81019

Summary: An equation of Newton-Nelson type on the vector bundle over space-time of General Relativity is introduced and investigated. The equation is interpreted as the one describing the motion of a quantum particle in the classical gauge field in the language of stochastic mechanics.

MSC:

81P20 Stochastic mechanics (including stochastic electrodynamics)
58J65 Diffusion processes and stochastic analysis on manifolds
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H30 Applications of stochastic analysis (to PDEs, etc.)
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References:

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