In quantum field theory, the Stone--von Neumann theorem cannot be applied. This implies the existence of an infinite set of inequivalent representations of canonical (anti)commutation relations. Among the others, the theory and the phenomenology of field mixing are affected by this property. In particular the flavor vacuum turns out to have an exotic condensate structure which implies low-energy corrections to the standard oscillation formula and related quantities. When one tries to take into account this non-trivial vacuum structure, the standard functional-integral tools such as generating functionals or transitional amplitudes, are often quite inadequate for such purposes. Here we show how to construct a generalized generating functional for Green's functions which allows to easily distinguish among a continuous set of vacua that are mutually connected via canonical transformations. Some applications are proposed, including translations and the mixing transformation for boson fields.