Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds

Abstract

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.

22 pages -- major revisions -- accepted in Annals of Global Analysis and Geometry

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Cited by in corpus (4)

• Hadamard states for quantized Dirac fields on Lorentzian manifolds of bounded geometry
• The quantization of Proca fields on globally hyperbolic spacetimes: Hadamard states and Møller operators
• The Quantization of Maxwell Theory in the Cauchy Radiation Gauge: Hodge Decomposition and Hadamard States
• Møller maps for Dirac fields in external backgrounds