Model for Topological Fermions

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 generalization of the Sine-Gordon model¹(We do not chase the aim to give a four-dimensional generalization of Coleman’s isomorphism between the Sine-Gordon model and the Thirring model which was shown in 2-dimensional space-time) from 1 + 1-dimensions to 3 + 1-dimensions, from S ¹ to S ³. For large distances from the centre 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.