Strong high-energy scattering in theories with weak coupling

The problem of the existence of strong nonperturbative scattering at high energy in theories with weak coupling is considered. It is shown that such scattering associated with multiboson production definitely exists in practically any theory with self-interacting bosons. An approach to this problem is proposed which is based on explicit splitting of the short-wave and the long-wave modes of the bosonic field and considering the process of excitation by the initial particles of the long-wave field to states with large energy. The nonperturbative analysis of the probability of excitation of the soft field to a large amplitude is based on the WKB technique developed in quantum mechanics for similar problems. It is also shown that the results of previous calculations can be reproduced within the proposed approach including those based on the analysis of instanton-induced amplitudes.