On Haag’s Theorem and Renormalization Ambiguities

Maiezza, Alessio; Vasquez, Juan Carlos (2021) On Haag’s Theorem and Renormalization Ambiguities. Foundations of Physics, 51 (4). ISSN 0015-9018

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Abstract

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.

Item Type:	Article
Uncontrolled Keywords:	quantum field theory; Haag's theorem; renormalization group; resurgence
Subjects:	NATURAL SCIENCES > Physics
Divisions:	Theoretical Physics Division
Projects:	Project title Project leader Project code Project type Fizika teraskale na LHC-u i u svemiru-TsPhLC Oleg Antipin IP-2016-06-4418 HRZZ
Depositing User:	Martina Žugaj
Date Deposited:	06 May 2026 11:42
URI:	https://fulir.irb.hr:/id/eprint/11910
DOI:	10.1007/s10701-021-00484-3

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