Geometrization of quantum formalism

TL;DR

This paper proposes a geometric interpretation of quantum mechanics, suggesting that the Dirac equation describes microscopic deviations in space geometry rather than point particles, unifying quantum behavior with space topology.

Contribution

It introduces a novel geometrical framework where quantum equations are group-theoretical relations of space topology, challenging traditional particle-based models.

Findings

Dirac equation interpreted as space geometry deviations

Electromagnetic gauge invariance derived from geometry

Atoms modeled without pointlike electrons

Abstract

The hypothesis is suggested that the equation for the Dirac free wave field is, in fact, a group-theoretical relation describing propagation of specific microscopic deviations of space geometry from the euclidean one (closed topological manifolds). The Dirac equation for a hydrogen atom can also be interpreted as a relation that accounts for the symmetry properties of a piece of curved space. Within the framework of this concept, atoms have no any pointlike particles (electrons) inside, and the gauge invariance of electromagnetic field proves to be the natural consequence of the basic principles of the proposed geometrical approach.