# Short Items

• The latest issue of the New York Review of Books has an article about the new Turing film, explaining in detail how it gets pretty much everything completely wrong about Turing and his story (see my review here). In related news, this week it was announced that the film is one of the final Oscar nominees for Best Adapted Screenplay.
• The DESY research magazine femto has a sequence of articles about the LHC, SUSY and BSM physics.
• The Swedish Research Council has just announced a ten-year grant of $60 million SEK (about$7 million) to bring Frank Wilczek to Stockholm University.
• Mike Duff has some complaints about the Dean Rickles “A Brief History of String Theory” (for mine, see here.)
• Jim Stewart, a mathematician who became wealthy based on his popular Calculus book (which we use here at Columbia) passed away last month at the age of 73. For more about him, see here and here. I had the pleasure of meeting him a couple times, with one occasion including a tour of his remarkable home in Toronto, Integral House.
• For a new book about a certain mathematical point of view on QFT, see Factorization algebras in quantum field theory, by Kevin Costello and Owen Gwilliam.
• Quanta magazine has a nice article by Kevin Hartnett on Ciprian Manolescu’s work on the triangulation conjecture.

Update:
One more. The Yale Art Gallery now has an exhibition of prints based on equations chosen and drawn by well-known mathematicians and physicists. It’s called The Art of the Equation, and impresario of the project Dan Rockmore will be discussing it there at 5:30 on Thursday January 22.

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### 23 Responses to Short Items

1. editors says:

Dr. Woit,

We’ve been running a website that excerpts one old paper in the mathematical sciences per day. About a quarter of the posts are related to physics. Unfortunately, the physics posts don’t seem to get much attention from the physics community. Understandably old physics is only of interest to a minority of the physics community, but if you know anyone who is interested in that sort of the thing please feel free to share the following:

http://www.mathmarauder.com/archives/category/field/physics

2. Wow! That maths marauder website is great.
Amazing to see relativity discussed like this in 1904, and from this perspective. I think the difference is that AE started from the opposite end; ff you assume with a universal speed of light as a principle, what does that imply about space and time?
Great website..

3. Anonymous says:

Hi Peter,

Do you have an opinion about the approach used in Costello and Gwilliam’s work?

4. Peter Woit says:

Anonymous,
My opinion is that I wish I understood it better…

5. CHRIS says:

Anyone can comment/explain the difference between the axiomatic QFT approach (nets of observables/C* algebra etc..) which is actively pursued by some european universities now and factorization algebra approach pursued by Owen,Grady,Costello ? I been reading AQFT (Haag) on my own and I didn’t feel comfortable with the axiomatic approach at all and the math there. BTW , i am not bias.
Thanks

6. gossip says:

Do you have some more details on the Wilczek item? Will he be relocating to Stockholm full-time? Or only a few months per year?

7. Peter Woit says:

gossip,

From this
where he refers to “visiting” Stockholm in June I assumed it isn’t a full-time move, but I don’t know.

8. I’d love to look at the mathmarauder page, but it has been unreachable since yesterday (and I have been too lazy to use the web archive/wayback machine). I hope that page is going to continue – it sounds fun and informative.

9. Anonymous says:

Chris,

Perhaps the biggest difference is that the axiomatic treatments you’re referring to are in Lorentzian signature, whereas Costello-Gwilliam are in Euclidean. As a consequence, the algebra of observables in these two situations satisfy different properties.

10. @Chris and Anonymous

I think the main difference is that the Costello-Gwilliam approach is in the setting of formal power series in “h bar”. The axiomatic/algebraic approach a priori is non-perturbative although recently it has developed a sub-area addressing pertubative renormalization etc. ; see for instance the recent work of Katarzyna Rejzner and references therein. The difference between Lorentzian and Euclidean signatures is not that big a deal, especially because the precise connection is given by the Osterwalder-Schrader Theorem which is a result from axiomatic QFT.

11. timothy212 says:

Dear all
Can anyone illustrate on the prospect of various constructive quantum field theory like
1.) Axiomatic approach
2.) Owen Costello approach
3) topological qft
4) Balaban approach
5) others ..
and how far each one is from constructing the ultimate 4 dimension interacting qft and also the mass gap problem
One interesting thing is it seems like the
Axiomatic approach is mainly pursued
By European universities and almost no
US researchers doing that .
Do you guys know why ?
Thanks

Tim

12. @Abemalek,

Just a quick note. The difference between Lorentzian and Euclidean is a big deal if the background you are interested in is not Minkowski space (or, more generally does not have a nice timelike Killing vector). In the absence of such time translation symmetry there is no known analog of the Osterwalder-Schrader Theorem or even of the Euclidean formalism. And even just having a Killing vector is not enough (I believe the spacetime has to be static, and not just stationary), e.g., AFAIK QFT on Kerr does not have a Euclidean version.

13. @ Igr,

I didn’t make it explicit but I was talking about flat space.

14. @Abdemalek,

I’m well aware and my comment was aimed at the larger audience. And that’s fine if all that you are interested in is Minkowski space. However, it’s worth reminding people of the fragility of the link between the QFT formalisms in these different signatures, because the attitude of “Why bother with Lorentzian signature at all?” is troublingly common.

While I’m on the subject, another point that’s often overlooked is the relevance of this issue for non-perturbative QFT. Quite a number of people are happy to accept that lattice gauge theory provides a non-perturbative construction of QFT (or at least a path eventually leading to one). However, that method is contingent on the Euclidean formalism and hence breaks in non-static backgrounds, for which then there’s not even a suggestion of a method that could lead to a non-perturbative construction.

15. Bernhard says:

6M SEK per year for a grant including a Nobel Laureate is actually reasonable. Because of the large overhead costs at Swedish Universities, about 2 M SEK per year are needed just to cover his salary (given that you need about 1M just to cover a random postdoc). Given that he will need students and travel money for his team, 60M SEK end up not being extravagant.

16. Dean Rickles says:

Hi Peter,

I just read the Michael Duff review. Since his complaints make no sense at all and get things entirely the wrong way around, this is probably a good place to vent:

(1) He complains that I don’t explain how M-theory came to be. Yet I very explicitly noted in the preface that I was dealing with the earliest phases of string theory, and offer only a glimpse of M-theory, with considerably less detail involved.
(2) He says I “echo the Wikipedia version of the History of String Theory, according to which research on branes began only in 1995”. Nothing could be further from the truth. There is section after section, and footnote after footnote where I point out that most of the D-brane apparatus was discovered much earlier, going back to the late 1980s – including Duff’s work. I’m particularly annoyed at this one, since it was one of the key myths I wanted to correct. (Ditto his claim that I buy into the talk of “superstring revolutions” – another myth I explicitly argued against in the book)
(3) He says I only mention “membranes” in a “derisory” way – I’ve no idea where he gets this from. There is nothing in the least derisory about anything I say about them!
(4) Worst of all, he complains that I “belittle the role of supergravity” by referring to a “decade of darkness” in the 70s and 80s. But this is an ironic title! The whole point is to show that the ‘dark days of string theory’ is also a myth, and supergravity is identified as the central player in this story. Yet apparently I “downgrade supergravity” with “zeal”. That is a stunning statement given the pains I went to to tell exactly the opposite story.

Incidentally, my final paragraph contains the remark: “The lesson I think emerges from this is that, while the mythological presentations of ‘revolutions’ and ‘dark years’ and so on, make for a good story, a more accurate depiction reveals a somewhat less turbulent life story, though no less interesting for it.”

So I’m truly flummoxed by this review of Duff’s…

Best,
Dean

17. @Abdelmalek Abdesselam,

even on Minkowski spacetime/Euclidean space, it is not a priori clear how to apply Osterwalder-Schrader or any other result in Haag-Kastler-style AQFT to those factorization algebras. Because, while the conceptual idea is similar in both cases — to encode a QFT by its system of assignments of collection of observables to regions of spacetime (Heisenberg picture!, dual to the Schrödinger picture of say the cobordism hypothesis) — the technical implementation is quite a bit different. In those factorization algebras the “collection” of observables assigned to a spacetime region is not only not C*, but is not even an algebra at all, it is just a chain complex (a quantum deformed BV-complex ) without a product operation. The whole system of these chain complexes as the space region varies does inherit an operadic homotopy-algebra structure sort of globally by way of inclusion induced by spacetime regions into each other, but there is a priori no “net of algebras”, not even in Fredenhagen’s perturbative relaxation of the Haag-Kastler axioms.

There might be a good translation between these two formalizations of Heisenberg-picture stype QFT, and maybe once it’s there it would allow to transport results such as Osterwalder-Schrader from Haag-Kastler-style axiomatics to factorization algebras. But for the moment this is wide open, as far as I am aware.

18. Peter Woit says:

Hi Dean,
Glad to provide a venue for you to respond!

19. Tim Nguyen says:

@timothy212

Each of the approaches you mention are addressed at different aspects of QFT (topological, perturbative, constructive). Each have their own goals and limitations and as such are not as comparable as your question might suggest. For the axiomatic QFT you are asking about, the main goal seems to be to overcome the limitations of formulations QFT formulated on flat space, since our universe is curved not flat. Moreover, there is a Haag’s theorem which roughly says the usual interaction picture of QFT’s doesn’t exist, hence the emphasis of the axiomatic school on algebras of observables rather than their representations.

As for why it hasn’t caught on broadly, my guess is that it’s because 1) it’s still perturbative 2) it’s not relevant to the majority of interesting physics already taking place on flat space or on (compact) Euclidean manifolds.

But your question raises a good point: it’s clearly a sign that there is much to learn and much work to do in QFT when there are many disparate schools of QFT that don’t actively communicate. Any particular school will have its own problems internal to its own (e.g. if you are interested in TQFT, you can go off and study category theory and leave physics behind). On the other hand, I think real progress will be made once more emphasis is put on solving important framework-independent problems in QFT, e.g. mass gap, making sense of many of Witten’s remarkable results (which did not come about by adhering to any particular formalism).

20. Tim Nguyen says:

@Igor

If I understand correctly, couldn’t one just simulate QCD on a curved background by modifying Wilson’s lattice action to be plaquette dependent to account for a spatially varying metric?

21. Peter Woit says:

Tim,
Yes, you could do QCD on a curved Euclidean signature background as you suggest. I think the problem Igor is concerned about is that you lose the usual argument connecting the theory to a physical Minkowski signature theory.

For something related, I was going to give a link to a video of a lecture by Graeme Segal about Wick rotation

22. JG says:

Not sure if this is a good place to post this, but latest rumours are that the BICEP2/Planck analysis is out next week and there is no B-mode signal due to gravitational waves.

eg according to Peter Coles

Hearing that the #Planck/#Bicep2 cross-correlation results will be out next week (and the only B mode in CMB is from lensing, not GWs)

23. Peter Woit says:

More specific rumor I’ve seen is that this will be in an arXiv paper out Monday night.