Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds

Autor:	Murro, Simone, Volpe, Daniele
Rok vydání:	2020
Předmět:	Mathematics - Differential Geometry Mathematical Physics Mathematics - Analysis of PDEs Primary 53C50 58J45 Secondary 53C27 81T05
Zdroj:	Ann. Glob. Anal. Geom. 59, 1-25 (2021)
Druh dokumentu:	Working Paper
DOI:	10.1007/s10455-020-09739-0
Popis:	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. Comment: 22 pages -- major revisions -- accepted in Annals of Global Analysis and Geometry
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2004.03300 Zobrazit plný text záznamu View this record from Arxiv