Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-10-27
FewBodySyst.30:149-186,2001
Physics
High Energy Physics
High Energy Physics - Theory
42 pages, 7 figures, more detailed calculations and comparison to Skyrme model and 't Hooft-Polyakov monopoles added
Scientific paper
10.1007/s006010170009
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.
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