## Generalization
of relativistic particle dynamics on the case of

## non-Riemannian
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://gasdyn-ipm.ipmnet.ru/~rylov/yrylov.htm

Updated March 19, 2010

#### abstract

Conventional
relativistic dynamics of a pointlike particle is generalized on the case of
arbitrary non-Riemannian space-time geometry. Non-Riemannian geometry is an
arbitrary physical geometry, i.e. a geometry, described completely by the world
function of the space-time geometry. The physical geometry may be discrete, or
continuous. It may be granular (partly continuous and partly discrete). As a
rule the non-Riemannian geometry is nonaxiomatizable, because the equivalence
relation is intransitive. The dynamic equations are the difference equations.
They do not contain references to a dimension and to a coordinate system. The
generalization is produced on the dynamics of composite particles, which may be
identified with elementary particles. The granular space-time geometry
generates multivariant motion, which is responsible for quantum effects. It generates
a discrimination mechanism, which is responsible for discrete values of the
elementary particles parameters. The quantum principles appear to be needless
in such a dynamics..

There is
text of the paper in English (pdf, ps) and in Russian (ps, pdf)