标题： 量子场论的变形与相互作用模型的构造 显示英文标题

标题： Deformations of Quantum Field Theories and the Construction of Interacting Models

摘要： 本论文的主题是具有非平凡相互作用的QFT模型的严格构造。 在AQFT框架下讨论了两种不同的方法。 一方面，考虑了一个逆散射问题。 给定一个可分解的S矩阵作为构造的起点。 所考虑的粒子谱包括任意数量的带质量粒子种类，它们在全局规范群下变换。 从已知的楔形局部辅助场出发，展示了向局部理论的转变。 为此，我们利用了模态核性条件，并研究了由辅助场生成的楔形代数到所考虑的希尔伯特空间的某些映射。 在非常合理的假设下，证明了这些映射是核的，这意味着在有界区域相关的代数具有非平凡性，即Reeh-Schlieder性质成立。 通过这种方式可以构造出一大类1+1维具有可分解S矩阵的可积模型。 其中包括O(N)不变的非线性sigma模型。 另一方面，变形技术是一种可以在任意时空维度应用的构造方法。 这种方法从一个已知的量子场论模型出发，并对其进行某种修改。 具体来说，对一个标量带质量费米子模型进行了变形。 产生的模型基于楔形局部场，允许计算两粒子S矩阵。 得到的散射矩阵依赖于变形，并不同于初始模型的散射矩阵。 通过限制到1+1维，变形方法产生了一大类具有可分解S矩阵的可积模型，包括Sinh-Gordon模型。 显示英文摘要

摘要： The subject of this thesis is the rigorous construction of QFT models with nontrivial interaction. Two different approaches in the framework of AQFT are discussed. On the one hand, an inverse scattering problem is considered. A given factorizing S-matrix is thereby taken as the starting point of the construction. The particle spectrum taken into account involves an arbitrary number of massive particle species, transforming under a global gauge group. Starting from known wedge-local auxiliary fields, the transition to local theories is shown. To his end, we make use of the modular nuclearity condition and investigate certain maps from the wedge algebras, generated by the auxiliary fields, to the considered Hilbert space. Under a very plausible conjecture it is shown that these maps are nuclear, which implies the nontriviality of algebras associated with bounded regions in the sense that the Reeh-Schlieder property holds. A large class of integrable models with factorizing S-matrices in 1+1 dimensions can be constructed in this way. Among them are the O(N)-invariant nonlinear sigma-models. Deformation techniques, on the other hand, constitute a method of construction which may be applied in arbitrary spacetime dimensions. This approach starts from a known quantum field theoretic model which is subjected to a certain modification. Here, concretely, the model of a scalar massive Fermion was deformed. The emerging models are based on wedge-local fields, allowing for the computation of the two-particle S-matrix. The resulting scattering matrix depends on the deformation and differs from the one of the initial model. By restricting to 1+1 dimensions, the deformation method yields a large class of integrable models with factorizing S-matrices, including the Sinh-Gordon model.