On Haag's theorem and renormalization ambiguities

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 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.

arXiv commentFixed typo, version matches with the one in Foundations of Physics

References in corpus (10)

• The Magnus expansion and some of its applications
• Generating Non-perturbative Physics from Perturbation Theory
• An $S$-Matrix for Massless Particles
• Resurgence of the Renormalization Group Equation
• The Quantum Sine Gordon model in perturbative AQFT
• Non-local Lagrangians from Renormalons and Analyzable Functions
• Resummation and renormalons in a general Quantum Field Theory
• Non-Wilsonian ultraviolet completion via transseries
• Avoidance of a Landau Pole by Flat Contributions in QED
• Connected Chord Diagrams and the Combinatorics of Asymptotic Expansions

Cited by in corpus (5)

• Resurgence of the QCD Adler function
• A consistent quantum field theory from dimensional reduction
• The QCD Adler function and the muon $g-2$ anomaly from renormalons
• Canonical aspects of pregeometric vector-based first order gauge theory
• Quantum Field Theory on Multifractal Spacetime: Varying Dimension and Ultraviolet Completeness