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Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds
Annals of Global Analysis and Geometry ( IF 0.7 ) Pub Date : 2020-09-23 , DOI: 10.1007/s10455-020-09739-0
Simone Murro , Daniele Volpe

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.

中文翻译:

全局双曲流形上对称双曲系统的交织算子

在本文中,通过一系列交织算子实现了在(可能不同的)全局双曲流形上比较对称双曲系统解的几何过程。通过固定一个合适的参数,结果表明产生的交织算子保留了在齐次解空间上自然定义的厄米形式。作为一个应用,我们在代数量子场论的背景下研究了交织算子的作用。特别是,我们为全局双曲流形上所谓的哈达玛态的存在提供了新的几何证明。
更新日期:2020-09-23
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