### The Euclidean geometry deformations and capacities of their application to

### microcosm space-time geometry

#### Yuri A. Rylov

*Institute for Problems in Mechanics, Russian Academy of Sciences*

* 101-1 ,Vernadskii Ave., Moscow, 119526, Russia*

* email: rylov@ipmnet.ru*

Web site: http://rsfq1.physics.sunysb.edu/~rylov/yrylov.htm

or mirror Web site: http://195.208.200.111/~rylov/yrylov.htm

Updated October 11 , 2002

#### abstract

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 and T-geometry is nondegenerate and symmetric, 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.

There is text of the paper in __English__ and in __Russian__ and figures __1,2__, __3__, __4__