Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds

Simone Murro, Daniele Volpe
April 07, 2020
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.

Symmetric hyperbolic systems; Møller operator; Dirac operator; wave equation