An analogue of non-interacting quantum field theory in Riemannian signature
Abstract
In this paper, we define an analogue of non-interacting quantum fields satisfying (\Delta_{\mathbf{g}}-\lambda^{2})\phi=0 on a Riemannian scattering space (M,\mathbf{g}) with two boundary components, i.e., a manifold with two asymptotically conic ends (meaning asymptotic to the “large end” of a cone). Thus, the Lorentzian spacetime of usual QFT constructions is replaced by a Riemannian manifold with two boundary components, which play a role analogous to the two components of the mass shell for the Klein–Gordon field on Lorentzian spacetimes. Our main result describes a canonical construction of two-point functions satisfying a version of the Hadamard condition.
Fields of Study & Subjects
Advanced Mathematical Theories and Applications
Spectral Theory in Mathematical Physics
Quantum Mechanics and Non-Hermitian Physics
Publication details
- Journal / source
- Journal of Spectral Theory
- Volume
- 16
- Issue
- 3
- Pages
- 927–982
- Publication date
- 6 August 2026
- Language
- EN