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started Haag’s theorem, following a discussion with Todd, but am running out of time
Thanks, Urs. When you have more time: has Haag’s theorem sometimes been viewed as a motivation for the development of AQFT?
just telegraphically:
I rarely see AQFT texts point to Haag’s theorem in particular as a motivation, but the general context of the theorem has been a major motivation: lots of technical problems in QFT simply go away if one does not insist on forming the state spaces (hence the representations of the algebras of observables) Not the least for instance infrared problems in renormalization theory.
The idea is not that these problems cannot be actually solved, but that solving them is additional fine-grained information that can be looked at if desired, but that need not go into the axioms, hence the basic formulation of the theory.
I’ll try to give more details on this later.
(years later…)
I have added the missing cross-links between Haag’s theorem and canonical commutation relation
Is the \ldots
in
quantum fi…eld
on purpose?
thanks for the alert. looks like an artifact from copy-and-pasting out of a pdf. I have fixed it.
I have polished-up the original references in this entry, and added pointer to:
But looking over this entry I see that it fails to even mention the gist of Haag’s theorem, regarding interacting quantum field theories. I have added a warning on this omission at the end of the Idea-section; don’t have the nerve right now to do something about it.
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