Reflection Positive Doubles

TL;DR

This paper introduces reflection positive doubles, a comprehensive framework for reflection positivity applicable to various physical systems, providing conditions for positivity and practical tools for verification.

Contribution

It develops a unified framework for reflection positivity across different system types, with explicit conditions and interpretability in terms of coupling constants.

Findings

Provides necessary and sufficient conditions for reflection positivity.

Uses a reflection-invariant cone for construction and analysis.

Includes numerous illustrative examples.

Abstract

Here we introduce reflection positive doubles, a general framework for reflection positivity, covering a wide variety of systems in statistical physics and quantum field theory. These systems may be bosonic, fermionic, or parafermionic in nature. Within the framework of reflection positive doubles, we give necessary and sufficient conditions for reflection positivity. We use a reflection-invariant cone to implement our construction. Our characterization allows for a direct interpretation in terms of coupling constants, making it easy to check in concrete situations. We illustrate our methods with numerous examples.