Haag's theorem in renormalised quantum field theories

TL;DR

This paper reviews no-go results in axiomatic quantum field theory, focusing on Haag's theorem, and discusses how renormalisation circumvents it, raising questions about the consistency of interaction descriptions.

Contribution

It highlights the implications of Haag's theorem for quantum field theory and critiques how renormalisation bypasses the theorem's constraints.

Findings

Haag's theorem challenges the consistency of interaction descriptions in QFT.

Renormalisation bypasses Haag's theorem by violating unitarity.

Canonical perturbation theory is critiqued for its role in this bypass.

Abstract

We review a package of no-go results in axiomatic quantum field theory with Haag's theorem at its centre. Since the concept of operator-valued distributions in this framework comes very close to what we believe canonical quantum fields are about, these results are of consequence to quantum field theory: they suggest the seeming absurdity that this highly victorious theory is incapable of describing interactions. We single out unitarity of the interaction picture's intertwiner as the most salient provision of Haag's theorem and critique canonical perturbation theory to argue that renormalisation bypasses Haag's theorem by violating this very assumption.