Inconsistency of Minkowski higher-derivative theories

TL;DR

Minkowski higher-derivative quantum field theories are generally inconsistent due to nonlocal, non-Hermitian divergences that cannot be renormalized, especially when propagators have complex poles, affecting their physical viability.

Contribution

This paper demonstrates the inherent inconsistencies in Minkowski higher-derivative theories caused by complex poles and nonlocal divergences, challenging their use in quantum field theory.

Findings

Complex divergences arise in self-energies and three-point functions.

Standard power counting rules are invalidated in these theories.

Counterterms violate locality and Hermiticity in scalar and gravity models.

Abstract

We show that Minkowski higher-derivative quantum field theories are generically inconsistent, because they generate nonlocal, non-Hermitian ultraviolet divergences, which cannot be removed by means of standard renormalization procedures. By "Minkowski theories" we mean theories that are defined directly in Minkowski spacetime. The problems occur when the propagators have complex poles, so that the correlation functions cannot be obtained as the analytic continuations of their Euclidean versions. The usual power counting rules fail and are replaced by much weaker ones. Self-energies generate complex divergences proportional to inverse powers of D'Alembertians. Three-point functions give more involved nonlocal divergences, which couple to infrared effects. We illustrate the violations of the locality and Hermiticity of counterterms in scalar models and higher-derivative gravity.