For JC, the formalism reproduces the tree level amplitudes which is substantive in and of itself. Unfortunately, according to a followup by Berkovitz and Witten, it appears that the theory with loops will most likely reproduce the diagrams of conformal supergravity rather than those of N=4 SYM.

So, it seems likely at this point that the original proposal will not reproduce all of SYM, but, again, that doesn’t mean that there will be no future results on the subject. You can read Witten’s original big paper (the first half is all QFT — no string theory) for some intriguing facts about those loop amplitudes you referenced.

But, none of this changes the fact that the referenced paper is all about the very physical idea of doing scattering computations in Yang-Mills theory.

Do you know if anybody has been able to get Witten’s twistor formalism to work for the QCD 1-loop amplitudes and beyond?

If Witten’s twistor formalism has any substance in the end, it should be able to reproduce the 1-loop formulas found by Dixon, Kosower, & Bern during the 1990’s.

I am not claiming to be qualified to judge the details of this paper, but I would remind you that sooner or later conformal invariance must be broken as the world is quite obviously not conformally invariant. Penrose’s group worked for decades on ways of putting in masses and did not come up with anything very convincing. Maybe Witten’s team can do better, and I would be delighted if they could, but as things stand, this is a huge, and possibly insurmountable barrier.

Interesting math? That paper gives new ways of doing computations in QCD. I consider that pretty damn physical. Don’t you think that’s at least somewhat interesting?

You can’t compute everything using this method, but I’m really astounded that you immediately dismiss it as ‘interesting math’. Did you read the paper?

And how pessimistic is it to think that something in its initial stages will never be extended to compute diagrams involving things other than gluons?

Your comment frankly couldn’t be more inapposite.

I remember years ago stories about some younger particle theory professors attempting to teach quantum field theory (QFT) courses in a “modern” context.

There were guys who started off with the path integral on the first day, and didn’t really mention much of the old canonical quantization way of doing things. By the end of the 1st semester, they were already finished covering numerous tree level calculations in phi^4, QED, and even some electroweak and/or QCD Standard Model stuff. Some folks even got as far as covering the renormalization of phi^4 theory or even QED in the 1st semester!

After about a month or so into the 1st semester, almost all of the experimentalists were scared off and subsequently stopped attending the lectures and/or dropped the course. By the time it was the 2nd semester of the course, the only folks left mostly consisted of theory students interested in particle physics and/or condensed matter. Mid way through the 2nd semester, many of the condensed matter folks disappeared too.

It seems like teaching QFT starting off with the path integral is almost like the equivalent of “culture shock” for many students.

Thanks for that. Once again we see Witten et al, given a choice between physics and interesting math choosing the latter. Twistor space cannot deal with massive particles. This is unfortunate as not only is there clear experimental evidence for massive particles, but a lot of these masses have been measured to a high degree of precision. Maybe they can have massive particles as some kind of composite, but I am not aware of any developed theory that works on these lines. Maybe someone can prove me wrong – ?

http://xxx.lanl.gov/abs/hep-th/0403047

All QFT books are much of a muchness though and just present the usual sequence of stuff: free scaler, fermion, em fields, commutators, then Feynman-Dyson perturbation theory, S-matrix, phi^4 theory, QED, Feynman rules, vacuum polarisation etc. Then same results via path integrals, then renormalisation/regularisation. As a student, you never really get any clear or deep explanations in any text as to why you are even doing/learning this stuff in the first place.

I have never really enjoyed perturbation (it can also cause blindness:)or the whole Feynman-Dyson formalism. Quite tedious to learn. Amazingly, it works out though and lots of things can be computed to high accuracy in the end so students/authors don’t seem to question it or some of the underlying dodgy math. It is very entrenched in the theoretical physics culture so people like Chris who have chosen in the past to question aspects of it, won’t go down well with the establishment or journal editors. There is probably room for another QFT book if someone can put a new modern twist or approach on the subject with some vitality. Weinberg’s volumes were good but he is very much from the old school.

A big problem now though for the S-matrix formalism, and esp. for string theory, is you can’t actually define it on deSitter space, the space on which we appear to actually reside.