A Model for Topological Fermions

TL;DR

This paper presents a model where charged particles are stable topological solitons in a field with values on S^3, exhibiting relativistic properties and connecting to electromagnetic phenomena, extending the sine-Gordon model to 3+1 dimensions.

Contribution

It introduces a novel topological soliton model for charged particles in 3+1 dimensions, generalizing the sine-Gordon model and capturing relativistic and electromagnetic effects classically.

Findings

Solitons behave like relativistic particles with Lorentz contraction.

The model reproduces effects like particle-antiparticle annihilation.

At large distances, it reduces to a dual U(1) electromagnetic theory.

Abstract

We introduce a model designed to describe charged particles as stable topological solitons of a field with values on the internal space S^3. These solitons behave like particles with relativistic properties like Lorentz contraction and velocity dependence of mass. This mass is defined by the energy of the soliton. In this sense this model is a generalisation of the sine-Gordon model from 1+1 dimensions to 3+1 dimensions, from S^1 to S^3. (We do not chase the aim to give a four-dimensional generalisation of Coleman's isomorphism between the Sine-Gordon model and the Thirring model which was shown in 2-dimensional space-time.) For large distances from the center of solitons this model tends to a dual U(1)-theory with freely propagating electromagnetic waves. Already at the classical level it describes important effects, which usually have to be explained by quantum field theory, like particle-antiparticle annihilation and the running of the coupling.