2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/205651We prove general reflection positivity results for both scalar fields and Dirac fields on a Riemannian manifold, and comment on applications to quantum field theory. As another application, we prove the inequality $C_D \leq C_N$ between Dirichlet and Neumann covariance operators on a manifold with a reflection.11 pagesMathematical PhysicsAnalysis of PDEsDifferential GeometryFunctional Analysis81T20; 81T08; 58J05; 81Q10; 81Q70; 20F55text