Reflection positivity in higher derivative scalar theories

TL;DR

This paper rigorously demonstrates that a broad class of higher-derivative free scalar field theories violate reflection positivity, challenging their suitability for Euclidean-to-Lorentzian quantum field theory reconstruction.

Contribution

It provides a rigorous proof of reflection positivity violation in higher-derivative scalar theories with rational propagators, including degenerate cases.

Findings

Reflection positivity is violated in many higher-derivative scalar theories.

The violation applies to theories with rational propagators, including p^4-type.

This challenges the use of such theories in Euclidean quantum field frameworks.

Abstract

Reflection positivity constitutes an integral prerequisite in the Osterwalder-Schrader reconstruction theorem which relates quantum field theories defined on Euclidean space to their Lorentzian signature counterparts. In this work we rigorously prove the violation of reflection positivity in a large class of free scalar fields with a rational propagator. This covers in particular higher-derivative theories where the propagator admits a partial fraction decomposition as well as degenerate cases including e.g. p^4 -type propagators.