The Euclidean geometry deformations and capacities of their application to microcosm space-time geometry
| dc.creator | Rylov, Yuri A. | |
| dc.date | 2002-06-05 | |
| dc.date | 2002-09-13 | |
| dc.date.accessioned | 2026-07-07T05:47:40Z | |
| dc.date.available | 2026-07-07T05:47:40Z | |
| dc.description | Usually a Riemannian geometry is considered to be the most general geometry, which could be used as a space-time geometry. In fact, any Riemannian geometry is a result of some deformation of the Euclidean geometry. Class of these Riemannian deformations is restricted by a series of unfounded constraints. Eliminating these constraints, one obtains a more wide class of possible space-time geometries (T-geometries). Any T-geometry is described by the world function completely. T-geometry is a powerful tool for the microcosm investigations due to three its characteristic features: (1) Any geometric object is defined in all T-geometries at once, because its definition does not depend on the form of world function. (2) Language of T-geometry does not use external means of description such as coordinates and curves; it uses only primordially geometrical concepts: subspaces and world function. (3) There is no necessity to construct the complete axiomatics of T-geometry, because it uses deformed Euclidean axiomatics, and one can investigate only interesting geometric relations. Capacities of T-geometries for the microcosm description are discussed in the paper. When the world function is symmetric and T-geometry is nondegenerate, the particle mass is geometrized, and nonrelativistic quantum effects are described as geometric ones, i.e. without a reference to principles of quantum theory. When world function is asymmetric, the future is not geometrically equivalent to the past, and capacities of T-geometry increase multiply. Antisymmetric component of the world function generates some metric fields, whose influence on geometry properties is especially strong in the microcosm. | |
| dc.description | 49 pages, 4 figures, correction of misprints | |
| dc.identifier | https://arxiv.org/abs/physics/0206017 | |
| dc.identifier | http://arxiv.org/abs/physics/0206017 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/84739 | |
| dc.subject | General Physics | |
| dc.title | The Euclidean geometry deformations and capacities of their application to microcosm space-time geometry | |
| dc.type | text |