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We revisit the implications of Haag's theorem in the light of therenormalization group. There is still some lack of discussion in the literatureabout the possible impact of the theorem on the standard (as opposite ofaxiomatic) quantum field theory, and we try to shed light in this direction.Our discussion then deals with the interplay between Haag's theorem andrenormalization. While we clarify how perturbative renormalization (for thesub-class of interactions that are renormalizable) marginalizes the its impactwhen the coupling is formally small, we argue that a non-perturbative andnon-ambiguous renormalization cannot be built if there is any reference to theinteraction picture with free fields. In other words, Haag's theorem should beregarded as a no-go theorem for the existence of a non-ambiguous analyticcontinuation from perturbative to non-perturbative QFT.

On Haag's theorem and renormalization ambiguities