Vaccum interaction between topological objects

点击翻译按钮获取中文摘要

Topological solitons belong to the most interesting topics in quantum field theory as models for extended objects like strings, domain walls and baryons. The interaction of these objects, especially the scattering on off another, follows from their properties as classical fields. In addition, there is an interaction due to the vacuum fluctuations of quantum fields coupled to the background of the topological solitons. This is a vacuum interaction in complete analogy to the Casimir effect between conducting surfaces. The investigation of this interaction was so far nearly impossible due to the inherent ultraviolet divergences present in the intermediate steps and the complicated procedure of their removal. The situation changed with the appearance some years ago of the new T-matrix representation of the vacuum interaction energy. It allows to compute the Casimir force between objects of complicated shape with moderate computational effort. It is the aim of the present project to use the T-matrix representation as a method for the calculation of the vacuum interaction of topological solitons. Objects for the applications of this method are the known (1+1)-dimensional kinks and their lifting to domain walls, the interaction of vortex lines like Abrikosov-vortices, and of monopole solutions, the Skyrmion for instance.