How Haag-tied is QFT, really?

TL;DR

This paper critically examines Haag's theorem in quantum field theory, analyzing various responses and their implications for the foundations of physics and the construction of interacting fields.

Contribution

It develops a conceptual framework to assess different viewpoints on Haag's theorem, highlighting underlying philosophical and mathematical issues.

Findings

Reveals diverse interpretations of Haag's theorem

Highlights the importance of foundational questions in physics

Suggests a need for reevaluation of standard QFT constructions

Abstract

Haag's theorem cries out for explanation and critical assessment: it sounds the alarm that something is (perhaps) not right in one of the standard way of constructing interacting fields to be used in generating predictions for scattering experiments. Viewpoints as to the precise nature of the problem, the appropriate solution, and subsequently-called-for developments in areas of physics, mathematics, and philosophy differ widely. In this paper, we develop and deploy a conceptual framework for critically assessing these disparate responses to Haag's theorem. Doing so reveals the driving force of more general questions as to the nature and purpose of foundational work in physics.