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You must remove the functional arbitrariness from the RG-equations when you return to the physical theory.
Because of that process, the RG-equations transform to identities, and the "ghost states" completely disappear from the conventional models of the Quantum Field Theory.
This transition is equivalent to imposing a "natural boundary condition" to the asymptotical behavior of the effective interaction.
As always in mathematical physics, then something new appears:
the non-perturbative asymptotically free solution pops up.
See the text.