LATTICE APPROACH TO INTEGRABLE QUANTUM FIELD THEORIES AND APPLICATIONS

我们考虑共形量子场论和可积大质量量子场论，从它们的六顶点模型提供的晶格正则化出发。在以前的工作中，我们已经完全澄清了这个模型的相关函数的结构。我们可以通过（准）定域算符空间上隐藏的费米结构来解释之前观察到的它们的因式分解。在这个项目中，我们将研究费米结构的不同标度极限。对于共形场论，我们要表明，这种结构的标度极限诱导的基础上的Verma模。我们计划在此基础上研究运营商产品的扩展。我们期望共形块的递归关系在此基础上得到简化。为了实现我们的目标，我们必须将Jimbo，Miwa和Smirnov的六顶点模型的因式分解定理从相关函数推广到形状因子。如果这是成功的，我们将有一个新的和直接访问的相关函数的Sine-Gordon模型。

We consider conformal quantum field theories and integrable massive quantum field theories starting from their lattice regularizations provided by the six-vertex model. In previous work we have completely clarified the structure of the correlation functions of this model. We could explain their factorization that was observed before, by means of a hidden Fermionic structure on the space of (quasi-) local operators. In this project we will study different scaling limits of the Fermionic structure. For conformal field theories we want to show that the scaling limit of this structure induces a basis on the Verma moduls. We plan to study the operator product expansion in this new basis. We expect that the recursion relation for the conformal blocks will simplify in this basis. To achieve our goal we will have to generalize the factorization theorem for the six-vertex-model of Jimbo, Miwa and Smirnov from correlation functions to form factors. If this is successful we will have a new and direct access to the correlation functions of the Sine-Gordon model.