论文标题
代数量子场理论和因果对称空间
Algebraic Quantum Field Theory and Causal Symmetric Spaces
论文作者
论文摘要
在本文中，我们回顾了我们有关对称空间的因果结构以及代数量子场理论的几何方面的最新工作。由与von Neumann代数网络相关的模块化组的一些一般结果的动机，我们专注于Lie代数的Euler元素，即伴随作用定义3级毕业的元素。我们研究了它们在相应的因果对称空间中确定的楔形区域，并描述了在因果对称空间上构建von Neumann代数网的一些方法，这些方法满足了Reeh-Schlieder和Bisognano-Wichmann条件的抽象版本。
In this article we review our recent work on the causal structure of symmetric spaces and related geometric aspects of Algebraic Quantum Field Theory. Motivated by some general results on modular groups related to nets of von Neumann algebras,we focus on Euler elements of the Lie algebra, i.e., elements whose adjoint action defines a 3-grading. We study the wedge regions they determine in corresponding causal symmetric spaces and describe some methods to construct nets of von Neumann algebras on causal symmetric spaces that satisfy abstract versions of the Reeh--Schlieder and the Bisognano-Wichmann condition.
