Reflection Positivity and Monotonicity

Abstract

We 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 $C_D\le C_N$ between Dirichlet and Neumann covariance operators on a manifold with a reflection.

11 pages

References in corpus (3)

• Essential self-adjointness of Schroedinger type operators on manifolds
• Quantum Field Theory on Curved Backgrounds, I. The Euclidean Functional Integral
• Markov quantum fields on a manifold

Cited by in corpus (7)

• Higher Derivative Scalar Quantum Field Theory in Curved Spacetime
• Non-existence of Skyrmion-Skyrmion and Skyrmion-anti-Skyrmion static equilibria
• Reflection positivity in higher derivative scalar theories
• Reflection positivity for the circle group
• Instability of enclosed horizons
• A Construction of Euclidean Invariant, Reflection Positive Measures on a Compactification of Distributions
• Infinite volume limits in Euclidean quantum field theory via stereographic projection