LATTICE APPROACH TO INTEGRABLE QUANTUM FIELD THEORIES AND APPLICATIONS

可积量子场理论和应用的格子方法

• 批准号: 281507754
• 负责人: Professor Dr. Hermann Boos
• 金额: --
• 依托单位: Arbeitsgruppe Kondensierte Materie
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/281507754?language=en
• 关键词: LATTICE; APPROACH; INTEGRABLE; QUANTUM; FIELD

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.

我们考虑从六佛特克斯模型提供的晶格正规化开始的共形量子场理论和可集成的大量量子场理论。在先前的工作中，我们完全阐明了该模型的相关函数的结构。我们可以通过（准）本地操作员空间上隐藏的费米斯结构来解释它们之前观察到的分解。在这个项目中，我们将研究费米子结构的不同缩放限制。对于共形场理论，我们要证明该结构的缩放限制会导致Verma Moduls的基础。我们计划以新的基础研究运营商产品扩展。我们期望在此基础上简化保形块的递归关系。为了实现我们的目标，我们将不得不从相关函数到形式的六个vertex模型的分解定理概括。如果这是成功的，我们将有一个新的直接访问正弦模型的相关函数。