Haag's Theorem: Importance & Implications in QFT

[rkastner]

Yes (though I might express it more generally in terms of constructing an interacting representation of the Poincare group).

Do you merely assume this is always possible? If it is possible, then one has diagonalized the full Hamiltonian and the whole problem is solved. But the point of constructive QFT is to prove rigorously whether this is possible.

No -- I do indeed understand that the state spaces associated with the free and interacting theories are unitarily inequivalent.

Thanks for your interest. In this part of the paper I am simply restating the usual heuristic account of Haag's theorem, which is sufficient for the intended purpose of the paper. Again the referee did not seem to find this to be an issue.

 

[strangerep]

Thanks for your interest. In this part of the paper I am simply restating the usual heuristic account of Haag's theorem, which is sufficient for the intended purpose of the paper. Again the referee did not seem to find this to be an issue.

You did not answer my question.

 

[rkastner]

Part of the problem might just be one of communication. E.g., I have been sent on far too many wild goose chases in the past, so I'm now quite wary of spending a lot of time delving through old resources, reworking/checking their calculations, sorting out what is correct and what is merely claim. From the references you've posted here, it seems one must delve through a disparate collection of old papers, apply a sorting algorithm, and hopefully find a new theory which at least reproduces the vast array of results of standard QFT. (And let's not forget the multidecade wild goose chases of string theory and its progeny.)

If you believe so strongly in this, perhaps you should write a comprehensive modern review pulling all the pieces together more thoroughly than a few brief papers can do. It would have to cover (the equivalent of) the gory scattering calculations in, say, Peskin & Schroeder and other QFT textbooks, as well as some higher order results equivalent to modern 2-loop computations, and show that the usual divergences do not arise.

My paper is narrowly focused on proposing a way around the difficulties presented by Haag's theorem for standard QFT. I do think that eliminating the infinite independent degrees of freedom of the field is a way forward (as did Wheeler in the context of quantum gravity). You are of course welcome to submit a reply challenging the conclusions in my paper if you think they are flawed or overreaching, as you seem to be indicating here.
Best wishes, RK

 

[strangerep]

You are of course welcome to submit a reply challenging the conclusions in my paper if you think they are flawed or overreaching, as you seem to be indicating here.

Well, I was trying to make a constructive suggestion.

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

 

[bhobba]

You did not answer my question.

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.

Thanks
Bill

 

[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.