Reflection Positivity and Monotonicity

Arthur Jaffe, Gordon Ritter

Published 2007-05-04, updated 2007-05-09Version 2

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