Gliklikh, Yuri E.; Vinokurova, Natalia V. On the description of motion of a quantum particle in the classical gauge field in the language of stochastic mechanics. (English) Zbl 1315.81019 Commun. Stat., Theory Methods 40, No. 19-20, 3630-3640 (2011). 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. Cited in 1 ReviewCited in 1 Document 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.) Keywords:gauge field; Nelson’s stochastic mechanics; quantum particle PDFBibTeX XMLCite \textit{Y. E. Gliklikh} and \textit{N. V. Vinokurova}, Commun. Stat., Theory Methods 40, No. 19--20, 3630--3640 (2011; Zbl 1315.81019) Full Text: DOI References: [1] Belopolskaya Ya. I., Stochastic Processes and Differential Geometry (1989) · Zbl 1022.58016 [2] Bishop R. L., Geometry of Manifolds (1964) · Zbl 0132.16003 [3] DOI: 10.1007/3-540-09532-2_72 · doi:10.1007/3-540-09532-2_72 [4] Elworthy K. D., Stochastic Differential Equations on Manifolds 70 (1982) · Zbl 0514.58001 [5] Gliklikh Yu. E., Collection of Articles by Undergraduate and Posgraduate Students of Mathematical Faculty of Voronezh State University pp 36– (1999) [6] Gliklikh Yu. E., Nonlinear Analysis in Geometry and Topology pp 99– (2000) [7] DOI: 10.1007/978-0-85729-163-9 · Zbl 1216.58001 · doi:10.1007/978-0-85729-163-9 [8] DOI: 10.1007/BF02770538 · doi:10.1007/BF02770538 [9] DOI: 10.1103/PhysRev.150.1079 · doi:10.1103/PhysRev.150.1079 [10] Nelson E., Quantum Fluctuations (1985) [11] Parthasarathy K. R., Introduction to Probability and Measure (1978) [12] DOI: 10.1209/0295-5075/13/1/003 · doi:10.1209/0295-5075/13/1/003 [13] Zastawniak T., Proceedings of Swansea Conference on Stochastic Mechanics pp 280– (1992) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.