Asymmetric Nondegenerate Geometry

TL;DR

This paper explores asymmetric nondegenerate geometry (T-geometry) with a nonsymmetric world function, revealing new structures like multiple geodesics and tubes, and suggesting implications for microcosm physics and elementary particle theory.

Contribution

It introduces a novel asymmetric T-geometry framework that extends traditional geometry and links geometric features to particle physics concepts.

Findings

Three sorts of geodesics and tubes emerge from the antisymmetric component.

Finite timelike tubes suggest a geometric basis for confinement.

Associations between geometric structures and particle properties are proposed.

Abstract

Nondegenerate geometry (T-geometry) with nonsymmetric world function is considered. In application to the space-time geometry the asymmetry of world function means that the past and the future are not equivalent geometrically. T-geometry is described in terms of finite point subspaces and world function between pairs of points of these subsets, i.e. in the language which is immanent to geometry and free of external means of description (coordinates, curves). Such a description appears to be simple and effective even in the case of complicated T-geometry. Antisymmetric component of the world function generates appearance of additional metric fields. This leads to appearance of three sorts of Christoffel symbols and three sorts of geodesics. Three sorts of the first order tubes (future, past and neutral) appear. If the fields connected with the antisymmetric component are strong enough, the timelike first order tube has a finite length in the timelike direction. It was shown earler that the symmetric T-geometry explains non-relativistic quantum effects without a reference to principles of quantum mechanics. One should expect that nonsymmetric space-time T-geometry is also characteristic for microcosm, and it will be useful in the elementary particle theory, because there is a series of unexpected associations. First order tubes are associated with world tubes of closed strings. Antisymmetry is associated with supersymmetry. Three sorts of tubes are associated with three sorts of quarks. Limitation of the tube in time direction is associated with confinement. At any rate, the space-time T-geometry with additional parameters has more capacities, than usual Riemannian geometry.