Reflection Positivity and Monotonicity

TL;DR

This paper establishes reflection positivity results for scalar and Dirac fields on Riemannian manifolds and explores their implications in quantum field theory, including covariance operator inequalities.

Contribution

It provides new general reflection positivity theorems for scalar and Dirac fields and demonstrates an inequality between Dirichlet and Neumann covariance operators.

Findings

Reflection positivity results for scalar and Dirac fields

Inequality C_D ≤ C_N between covariance operators

Applications to quantum field theory

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