Description
The inclusion of higher derivatives is a necessary condition for a renormalizableor 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 show that these requirements for a consistent The inclusion of higher derivatives is a necessary condition for a bulding a 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 show that these requirements of a consistent quantum theory are satisfied in a high derivative theory recently proposed. This theory is based on a six-derivative scalar field action featuring a pair of ghost fields with complex conjugated masses that form a bound state. These results support the interpretation that physical observables can emerge from ghost dynamics in a consistent and unitary framework.