论文标题
超级希尔伯特空间和费米金功能场理论中拉格朗日对应的类别
Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory
论文作者
论文摘要
在本文中，我们研究了希尔伯特空间之间的拉格朗日对应关系。一个主要重点是当两个拉格朗日信件的组成再次是拉格朗日时期的问题。我们的答案尤其是在涉及的希尔伯特空间极化的一类拉格朗日信函中定义明确的构图定律。作为一种应用，我们在该类别的Lagrangian对应关系中具有值的几何旋转歧管上构建了功能性场理论，可以将其视为与自由费米斯粒子相关的理论的正式灯芯旋转。
In this paper, we study Lagrangian correspondences between Hilbert spaces. A main focus is the question when the composition of two Lagrangian correspondences is again Lagrangian. Our answer leads in particular to a well-defined composition law in a category of Lagrangian correspondences respecting given polarizations of the Hilbert spaces involved. As an application, we construct a functorial field theory on geometric spin manifolds with values in this category of Lagrangian correspondences, which can be viewed as a formal Wick rotation of the theory associated to a free fermionic particle in a curved spacetime.
