Geometrisation of electromagnetic interaction

TL;DR

This paper introduces a novel geometric framework for electromagnetic interactions by modeling Maxwell's and Dirac's fields within a unified non-Euclidean, non-Riemannian 4-manifold, linking physical properties to geometric features.

Contribution

It proposes a new geometric approach that unifies electromagnetic and quantum fields in a single curved space-time manifold, providing a geometric basis for particle properties.

Findings

Dirac's equation relates to the topology and metric of the manifold.

Electromagnetic fields are represented as curvature components.

Particle properties emerge as geometric characteristics.

Abstract

A new concept for the geometrisation of electromagnetic interaction is proposed. Instead of the concept "extended field--point sources", interacting Maxwell's and Dirac's fields are considered as a unified closed noneuclidean and nonriemannean space--time 4-manifold. This manifold can be considered as geometrical realisation of the "dressed electron" idea. Within this approach, the Dirac equation proves to be a relation that accounts for topological and metric characteristics of this manifold. Dirac's spinors serve as basis vectors of its fundamental group representation, while the electromagnetic field components prove to be components of a curvature tensor of the manifold covering space. Energy, momentum components, mass, charge, spin and particle--antiparticle states appear to be geometrical characteristics of the above manifold.