论文标题
非紧密因果对称空间中的楔形域
Wedge domains in non-compactly causal symmetric spaces
论文作者
论文摘要
本文是一个正在进行的项目的一部分，该项目针对均质空间的因果结构之间的联系，代数量子场理论（AQFT），操作员代数的模块化理论和谎言组的单一表示。在本文中，我们专注于非紧密因果对称空间$ g/h $。该类包含DE Sitter空间，还有其他具有不变部分订购的空间。 中心成分是\ fg的lie代数中的欧拉元素h。我们根据h/h上的H和因果结构定义三种不同类型的楔形域。我们的主要结果是，包含那些看似不同域的基点EH的连接组件都同意。此外，我们讨论了这些楔形域的联系。我们表明，这些空间中的每个空间都具有G_ \ c/g^C形式的非紧密因果对称空间的自然延伸，其中G^C是G。G_\ C/G^C的I I综合G _ \ $的某些真实形式，因为G_ \ c/g^c是非compactly Compactly Coctally Causal，它也带有三种类型的楔形域。我们的结果表明，这些域与$ g/h $的交集与g/h中的楔形域一致。
This article is part of an ongoing project aiming at the connections between causal structures on homogeneous spaces, Algebraic Quantum Field Theory (AQFT), modular theory of operator algebras and unitary representations of Lie groups. In this article we concentrate on non-compactly causal symmetric space $G/H$. This class contains the de Sitter space but also other spaces with invariant partial ordering. The central ingredient is an Euler element h in the Lie algebra of \fg. We define three different kinds of wedge domains depending on h and the causal structure on G/H. Our main result is that the connected component containing the base point eH of those seemingly different domains all agree. Furthermore we discuss the connectedness of those wedge domains. We show that each of those spaces has a natural extension to a non-compactly causal symmetric space of the form G_\C/G^c where G^c is certain real form of the complexification G_\$ of G. As G_\C/G^c is non-compactly causal it also comes with the three types of wedge domains. Our results says that the intersection of those domains with $G/H$ agrees with the wedge domains in G/H.
