  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. p^4 -type
propagators.
