LATTICE APPROACH TO INTEGRABLE QUANTUM FIELD THEORIES AND APPLICATIONS

我们从六顶点模型提供的晶格正则化出发，研究了共形量子场论和可积质量量子场论。在以前的工作中，我们已经完全阐明了该模型的关联函数的结构。我们可以通过(准)局部算符空间上隐藏的费米子结构来解释以前观察到的它们的因式分解。在这个项目中，我们将研究费米子结构的不同标度极限。对于共形场理论，我们想要证明这种结构的标度极限是基于Verma模的基。我们计划在这个新的基础上研究运营商的产品扩展。我们期望共形块的递推关系在此基础上得到简化。为了实现我们的目标，我们将不得不将吉博、米瓦和斯米尔诺夫的六顶点模型的因式分解定理从关联函数推广到形式因子。如果这是成功的，我们将有一个新的和直接的访问Sine-Gordon模型的关联函数。

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.