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