Universal Journal of Physics and Application Vol. 6(4), pp. 605 - 628
Reprint (PDF) (242Kb)

GENERALIZATION OF RELATIVISTIC PARTICLE DYNAMICS ON THE CASE OF NON-RIEMANNIAN SpACE-TIME GEOMETRY

AUTHOR(S) INFORMATION: Rylov Y. A.

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 e ects. 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.