Reflection positivity in a higher-derivative model with physical bound states of ghosts

TL;DR

This paper investigates a six-derivative scalar field theory with ghost fields, demonstrating that reflection positivity and spectral conditions are satisfied, supporting the possibility of a consistent, unitary quantum theory with ghost bound states.

Contribution

It shows that a higher-derivative scalar model with ghost bound states can satisfy reflection positivity, indicating potential for a consistent quantum gravity framework.

Findings

Reflection positivity holds in the model.

Ghost fields form bound states with physical implications.

Supports unitarity in higher-derivative theories.

Abstract

The inclusion of higher derivatives is a necessary condition for a renormalizable or superrenormalizable local theory of quantum gravity. On the other hand, higher derivatives lead to classical instabilities and a loss of unitarity at the quantum level. A standard way to detect such issues is by examining the reflection positivity condition and the existence of a Kallen-Lehmann spectral representation for the two-point function. We demonstrate that these requirements for a consistent quantum theory are satisfied in a theory we have recently proposed. This theory is based on a six-derivative scalar field action featuring a pair of complex-mass ghost fields that form a bound state. Our results support the interpretation that physical observables can emerge from ghost dynamics in a consistent and unitary framework.