Inconsistency of Minkowski higher-derivative theories

Understand

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.