  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.
