Haag's Theorem: Importance & Implications in QFT

[atyy]

A quick question for those that know more about Haag's theorem than I do.

I get it shows there is no interaction picture in the normal petubative methods used. But does lattice gauge theory circumvent the theorem? A quick search showed most think it does. In that case its an issue of method rather than anything being actually wrong with our theories.

Apparently a lattice theory does not necessarily circumvent the theorem, eg. http://d-scholarship.pitt.edu/8260/ p64

However, some Galilean QFTs do evade it.

In practice, if one assumes the lattice to be large but finite volume and with small but finite spacing, one can recover almost all known physics. The big problem for lattice methods is chiral fermions :(

Feynman should have said: I think it is safe to say that nobody understands chiral fermions :P

 

[TrickyDicky]

In practice, if one assumes the lattice to be large but finite volume and with small but finite spacing, one can recover almost all known physics. The big problem for lattice methods is chiral fermions :(

Feynman should have said: I think it is safe to say that nobody understands chiral fermions :P

I'd say fermions are involved in a great part of known physics, ;)

 

[rkastner]

Well, I was trying to make a constructive suggestion.

But you seem to become defensive when I ask questions. OK, I will stop.

Strangerep, you've already told me that you're dissatisfied with my answer: "You didn't answer my question."
I presented the basic assumptions that go into deriving the heuristic form of Haag's theorem, but that doesn't seem to satisfy you. I regret that I was unable to do so, and I wish you well. I do welcome any constructive criticisms of my paper, but it's too late for me to do any kind of major rewriting at this point as it has been accepted in its final form. If you think there are any gross errors of fact or technical blunders, feel free to write to the journal, ijqf.org
Best wishes,
Ruth

 

[rkastner]

Follow up: now that I'm done being distracted by travel and associated activities, I get what these two were concerned about. Sorry for missing the point initially. The sentence in question was confusing and also somewhat redundant anyway. I've uploaded a corrected version (without the sentence) to the arxiv. Thanks to both of you for the suggestion for improvement of the paper.