Lattice simulations of electroweak sphaleron transitions in real time

We perform a numerical investigation of high temperature transitions involving the change of topological charge in the electro weak theory. Three-dimensional space is approximated by a lattice. The dynamics is followed in real time, not euclidian time. Transitions were observed in the phase with spontaneous symmetry breaking as well as in the phase with restored symmetry. We determine the rate Γ of fermion number non-conservation in electroweak theory in the phase with restored symmetry. There is no suppression and Γ=κ(αwT)4 with κ≅0.1-1.0. (orig.)