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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMay 31st 2010

stub for spin-statistics theorem. Just recording a first few references so far.

• CommentRowNumber2.
• CommentAuthorTim_van_Beek
• CommentTimeMay 31st 2010

Added an idea paragraph and the reference to the Guido/Longo paper.

• CommentRowNumber3.
• CommentAuthorIan_Durham
• CommentTimeMay 31st 2010

There’s a really nice discussion of this from a conceptual POV in Tony Zee’s Quantum Field Theory in a Nutshell.

• CommentRowNumber4.
• CommentAuthorTim_van_Beek
• CommentTimeMay 31st 2010

Sure, why not. Some people would say that handwaving of this kind does more harm than good, but I’m not one of them. (Where is the argument for spin 1/2 ? :-)

I’m not quite happy with the situation in the Haag-Kastler either, as far as I understand it, I think there should be an argument that is easier…

• CommentRowNumber5.
• CommentAuthorIan_Durham
• CommentTimeMay 31st 2010

@Tim: Are you referring to Zee’s conceptual description? Wasn’t sure.

• CommentRowNumber6.
• CommentAuthorTim_van_Beek
• CommentTimeJun 1st 2010

Yes, I mean the chapter II.4 Spin-Statistics Connection, subchapter “The price of perversity”: The problem with the kind of argument presented here is that there are several no-go theorems that say that the objects manipulated here cannot be made precise in certain ways, one of the best review papers in AQFT, Hans Halvorson, Michael Müger, “Algebraic Quantum Field Theory” (reference is on the AQFT page) lists some of these.

This leads some people working in AQFT to the conclusion that arguments like this should be avoided at all costs, even at an undergraduate level.

This reminds me of an anecdote about Heisenberg: First, he intended to study mathematics, but when he told the math professor whom he consulted in Göttingen about this (I forgot his name) that he had read “Raum, Zeit, Materie” by Weyl, the professor said: “Then you have been spoilt for mathematics anyway”. Heisenberg then went to Arnold Sommerfeld and decided to study physics instead…

• CommentRowNumber7.
• CommentAuthorIan_Durham
• CommentTimeJun 1st 2010
• (edited Jun 1st 2010)

Hmmm. Interesting. I’ve heard of the Halvorson/Müger paper but have never read it. I would be curious to know what kind of arguments we should be using with undergraduates. Personally, I prefer correctness over simplicity, but, on the other hand, I also prefer that the student have some level of actual understanding and not simply be able to parrot what I say. It’s a tough line to straddle (I sincerely hope people appreciate how hard it can be to teach undergraduates well - sometimes I feel as if undergraduate education gets treated as the “ugly duckling” as it were).

I like the Heisenberg anecdote, by the way. I went hunting for Weyl’s grave in Zürich in January but wasn’t able to find it (I found Pauli’s, Hopf’s, James Joyce’s, and Fritz Zwicky’s).

• CommentRowNumber8.
• CommentAuthorTim_van_Beek
• CommentTimeJun 1st 2010

I would be curious to know what kind of arguments we should be using with undergraduates.

My outdated answer is: When I was a student, theoretical QFT was an optional class on the way to the Diplom, so the professors would simply say “we will do it our way and anyone who does not like it does not have to attend” (which means that there were introductory classes in QFT starting with the definition of a $C^*$ algebra).

There has been a big reform recently, the Bologna process, which changed that. I do not know how they do it now.

• CommentRowNumber9.
• CommentAuthorzskoda
• CommentTimeJun 2nd 2010

Bologna is good change for bad universities and disaster for good, as every democracy-like change in a structured society is: detrimental for elite and good for the masses.

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeJun 2nd 2010

Bologna is good change for bad universities and disaster for good, as every democracy-like change in a structured society is: detrimental for elite and good for the masses.

From my experience, this is quite right.

There has been endless discussion about this in the press here. One simple fact seemed to be implicit in each and every contribution that I have read, but was never made explicit:

nowadays there are simply two different kind of people going to universities, for two different kinds of reasons: one group wants to enter academia, the other group wants a high-level professional education. The whole problem is that these two groups are not being distinguished.

• CommentRowNumber11.
• CommentAuthorIan_Durham
• CommentTimeJun 2nd 2010
• (edited Jun 2nd 2010)

The whole problem is that these two groups are not being distinguished.

I think that is generally true, but, oddly enough, students in my department tend to be undecided until sometimes their senior year. One former student actually went into industry, disliked it, and returned to academia to get his PhD.

We've been having this sort of discussion on campus all year in relation to our revised core curriculum and strategic plan. One thing we realized that we do really well is, in general, provide a well-rounded, classical education to future professionals, meaning, as a college, the majority of our students end up as professionals (this is not entirely true for physics, though) but have gotten a classical education grounded in philosophy, theology, science, art, etc.

I guess what I'm saying is that it is possible to do both and do both well. The problem is that most institutions don't take the time to try. Instead they focus on one or the other. In the professional category, they tend to (at least in this country) cater to student desires a little too much (i.e. it's like they're selling a product).

But, back on the original topic, I'm always looking for new and creative - but correct! - ways to teach complex things to undergraduates. Like I said somewhere before, undergraduate education tends to be like the "ugly duckling" in math and physics (at least in this country, anyway) but it's only doing the field a disservice to treat it as such.
• CommentRowNumber12.
• CommentAuthorTim_van_Beek
• CommentTimeJun 22nd 2010

I would like to mention that, after my question at mathoverflow here about the PCT and the spin-statistics theorem did not get an answer (was worth a try anyway), I asked Professor Rehren from the Göttinger AQFT group the same question, and he confirmed that the references cited on the nLab are pretty much the state of the art. (He also mentions some papers about CFT that I don’t know, I’ll have a look).

• CommentRowNumber13.
• CommentAuthorUrs
• CommentTimeJun 22nd 2010

Thanks, Tim!

• CommentRowNumber14.
• CommentAuthorIan_Durham
• CommentTimeJun 23rd 2010

By the way, I just read in a new QM text, that Feynman once challenged the physics/mathematics community to develop an elementary proof of the spin-statistics theorem. In 2002 the editor of the American Journal of Physics brought up Feynman’s challenge again as having gone unfulfilled. Apparently this is still the case.

• CommentRowNumber15.
• CommentAuthorTodd_Trimble
• CommentTimeJun 23rd 2010

“Elementary” is in the eye of the beholder. I think Feynman originally said (in response to a challenge) that he would would prepare a “freshman lecture” to explain the theorem, but eventually gave up. (“Freshman lecture” meaning something on the order of his famous lecture notes on physics.)

• CommentRowNumber16.
• CommentAuthorTim_van_Beek
• CommentTimeJun 23rd 2010

“Elementary” is in the eye of the beholder.

My concept of “simple” in this case is:

a) axioms used: Can I understand the physical motivation of those?

c) how easy is it to spot when and where and how which of the axioms are used in the proof?

For example, the Reeh-Schlieder theorem needs heavy math machinery like the SNAG-theorem and the edge-of-the-wedge theorem, but on the other hand it is very easy to see which axioms are used, and that e.g. the causality axiom is not (which is a little bit disappointing for anyone who thinks that the Reeh-Schlieder theorem violates causality and that we should change the causality axiom to dodge it).

…the editor of the American Journal of Physics brought up Feynman’s challenge again as having gone unfulfilled.

Ok, but is there any money in it?

• CommentRowNumber17.
• CommentAuthorIan_Durham
• CommentTimeJun 23rd 2010

@Tim: What happened to point b)? ;)

Ok, but is there any money in it?

Probably not, but if my nanotech startup takes off and I get rich (as opposed to simply delusional), I’ll sponsor a prize for it. :-)