论文标题
在全球双曲歧管上的对称双曲线系统的交织操作员
Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds
论文作者
论文摘要
在本文中，通过（可能不同）在全球双曲线歧管上比较（可能不同的）对称双曲线系统解决方案的几何过程是通过一系列相互交织的操作员来实现的。通过固定合适的参数，可以证明所得的相互交织的操作员保留了在均匀溶液空间上自然定义的Hermitian形式。作为应用程序，我们在代数量子场理论的背景下研究了交织运算符的作用。特别是，我们为在全球双曲线歧管上存在所谓的Hadamard状态提供了新的几何证明。
In this paper, a geometric process to compare solutions of symmetric hyperbolic systems on (possibly different) globally hyperbolic manifolds is realized via a family of intertwining operators. By fixing a suitable parameter, it is shown that the resulting intertwining operator preserves Hermitian forms naturally defined on the space of homogeneous solutions. As an application, we investigate the action of the intertwining operators in the context of algebraic quantum field theory. In particular, we provide a new geometric proof for the existence of the so-called Hadamard states on globally hyperbolic manifolds.
