Charges and Electromagnetic radiation as topological excitations

We discuss a model with stable topological solitons in Minkowski space with only three degrees of freedom, the rotational angles of a spatial Dreibein. This model has four types of solitons differing in two topological quantum numbers which we identify with electric charge and spin. The vacuum has a two-dimensional degeneracy leading to two types of massless excitations, characterised by a topological quantum number which could have a physical equivalent in the photon number.Comment: 9 page

A Model for Topological Fermions

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.Comment: 42 pages, 7 figures, more detailed calculations and comparison to Skyrme model and 't Hooft-Polyakov monopoles adde

Vortices, Confinement and Higgs fields

We review lattice evidence for the vortex mechanism of quark confinement and study the influence of charged matter fields on the vortex distribution.Comment: 10 pages, 6 eps figures, talk presented by M.F. at the 5th International Conference "Quark Confinement and the Hadron Spectrum", Gargnano, Italy, September 10-14, 200

Darwin term from maximal entropy randow walk

We derive the stationary Schr\"odinger equation for particles in a potential from a special diffusion process, maximal entropy random walk (MERW) on a lattice. All trajectories of same duration get in MERW the same weight. To second order in the lattice spacing we deduce from this diffusion process the Darwin term