  Effective theories are non-local at the scale of the eliminated heavy
particles modes. The gradient expansion which represents such non-locality must
be truncated to have treatable models. This step leads to the proliferation of
the degrees of freedom which renders the identification of the states of the
effective theory nontrivial. Furthermore it generates non-definite metric in
the Fock space which in turn endangers the unitarity of the effective theory.
It is shown that imposing a generalized KMS boundary conditions for the new
degrees of freedom leads to reflection positivity for a wide class of Euclidean
effective theories, thereby these lead to acceptable theories when extended to
real time.
