Vaccum interaction between topological objects

作为弦、域壁和重子等扩展对象的模型，拓扑孤子是量子场论中最有趣的主题。这些物体的相互作用，特别是对另一个物体的散射，源于它们作为经典场的性质。此外，由于与拓扑孤子背景耦合的量子场的真空涨落，还存在相互作用。这是一种真空相互作用，完全类似于导电表面之间的卡西米尔效应。到目前为止，由于中间步骤中存在固有的紫外线发散以及复杂的去除过程，对这种相互作用的研究几乎是不可能的。随着几年前真空相互作用能的新T矩阵表示的出现，情况发生了变化。它允许以中等的计算量计算复杂形状的物体之间的卡西米尔力。本项目的目的是使用T矩阵表示作为计算拓扑孤子真空相互作用的一种方法。这种方法的应用对象是已知的(1+1)维扭结及其对磁区壁的提升，涡旋线的相互作用，如Abrikosov涡旋，以及单极子解，例如Skyrmion。

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.