An analogue of non-interacting quantum field theory in Riemannian signature

Abstract

In this paper, we define a model of non-interacting quantum fields satisfying $({\Delta }_g-{\lambda }^2)\varphi =0$ on a Riemannian scattering space $(M,g)$ with two boundary components, i.e. a manifold with two asymptotically conic ends (meaning asymptotic to the "large end" of a cone). Our main result describes a canonical construction of two-point functions satisfying a version of the Hadamard condition.

42 pages; some typos and sign errors fixed, some remarks added. Final version