Long range dynamics and broken symmetries in gauge models. The Stueckelberg-Kibble model

The general algebraic features associated to long range dynamics like the problem of removing the infrared cutoff, the definition of the algebraic dynamics and the occurrence of variables at infinity, the essential localization (seizing of the vacuum), the effective dynamics and its covariance group (dynamical symmetry group), the generalization of Goldstone's theorem and the non-trivial Goldstone spectrum, the mass/energy gap generation by the non-trivial classical motion of the variables at infinity are explicitly shown in the Kibble model as a prototype of gauge models exhibiting the Higgs phenomenon. The relation between mass generation in the Higgs phenomenon and the plasma energy gap is also discussed. (orig.)