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 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.

我们根据重整化群重新审视 Haag 定理的含义。关于该定理对标准（与公理化相反）量子场论可能产生的影响，文献中仍然缺乏讨论，我们试图在这个方向上阐明。然后我们的讨论涉及 Haag 定理和重整化之间的相互作用。虽然我们阐明了微扰重整化（对于可重整化的交互子类）如何在耦合形式较小时边缘化其影响，但我们认为，如果有任何参考，则无法建立非微扰和非歧义的重整化与自由场的互动图片。换句话说，