Coupling constant dependence in a special model of nonlinear field theory with internal symmetry

Localized excitations in the form of solitary waves of the Klein-Gordon-equation with cubic nonlinearity in one space and time dimension are studied and the observable physical quantities are investigated with respect to their dependence on the coupling constant. A complete and consistent calculation is possible by imposing an U(1)-symmetry, i.e. using complex fields. Two dispersion branches occur, where the corresponding energies are regular in one and highly singular in the other case.Presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.