Reflection positivity in higher derivative scalar theories

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., p4-type propagators.