Inclusion of radiation in the CCM approach of the $\phi^4$ model

Abstract

We present an effective Lagrangian for the $\phi^4$ model that includes radiation modes as collective coordinates. The coupling between these modes to the discrete part of the spectrum, i.e., the zero mode and the shape mode, gives rise to different phenomena which can be understood in a simple way in our approach. In particular, the energy transfer between radiation, translation and shape modes is carefully investigated in the single-kink sector. Finally, we also discuss the inclusion of radiation modes in the study of oscillons. This leads to relevant phenomena such as the oscillon decay and the kink-antikink creation.