A geometric model in 3+1D space-time for electrodynamic phenomena

TL;DR

This paper develops a 3+1D geometric model that predicts electromagnetic phenomena using solitons and topological quantum numbers, aiming to unify particle properties with geometric structures.

Contribution

It introduces a novel 3D generalization of the Sine-Gordon model linked to the Skyrme and Wu-Yang models, connecting geometric solitons to fundamental particles and photons.

Findings

Stable solitonic excitations resemble electrons and positrons.

Photons are associated with Goldstone bosons and topological quantum numbers.

Model proposes a geometric interpretation of charge, spin, and photon number.

Abstract

With the idea to find geometric formulations of particle physics we investigate the predictions of a three dimensional generalisation of the Sine-Gordon model, very close to the Skyrme model and to the Wu-Yang description of Dirac monopoles. With three rotational degrees of freedom of spatial Dreibeins we formulate a Lagrangian and confront the predictions to electromagnetic phenomena. Stable solitonic excitations we compare with the lightest fundamental electric charges, electrons and positrons. Two Goldstone bosons we relate to the properties of photons. These particles are characterised by three topological quantum numbers, which we compare to charge, spin and photon number. Finally we conjecture some ideas for further comparisons with experiments.