The Newton–Nelson Equation on Fiber Bundles with Connections
| Autor: | N. V. Vinokurova, Yu. E. Gliklikh |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Vector-valued differential form 021103 operations research Applied Mathematics General Mathematics Connection (vector bundle) Mathematical analysis 0211 other engineering and technologies Clifford bundle 02 engineering and technology 01 natural sciences Principal bundle Frame bundle 010104 statistics & probability Mathematics::Algebraic Geometry Normal bundle Spinor field Unit tangent bundle 0101 mathematics Mathematics::Symplectic Geometry Mathematics Mathematical physics |
| Zdroj: | Journal of Mathematical Sciences. 225:575-589 |
| ISSN: | 1573-8795 1072-3374 |
| DOI: | 10.1007/s10958-017-3479-0 |
| Popis: | 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). Moreover, 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|