An assortment of news and links that may be of interest:

The Tevatron has achieved a record luminosity for a hadron collider: 1.41×10^{32}cm^{-2}sec^{-1}. This is higher than the best luminosity at the ISR at CERN, and that was a proton-proton collider. Getting to high luminosity at the Tevatron is a lot harder since one need to create and store an intense beam of antiprotons.

The proceedings of this year’s Lattice 2005 conference are now online.

Prior to the summer’s big algebraic geometry conference in Seattle, there was a Graduate Student Warm-Up Workshop at which there were some excellent expository talks, for which lecture notes are online. A couple of these talks were specifically relevant to physics (Jim Bryan’s and Ron Donagi’s), but they are all interesting and worth reading.

The Bulletin of the AMS has a new editor and will soon have a new cover. One article soon to appear is a short piece by Michael Atiyah on Mathematics: Art and Science which contains a very interesting explanation of his views on mathematical beauty. Another is a review article Floer Theory and Low Dimensional Topology by Dusa McDuff. Floer theory has its origins in Witten’s work on supersymmetry and Morse theory. McDuff goes over this, and explains recent results on Heegard Floer theory due to Peter Ozsvath and Zoltan Szabo. Ozsvath is my colleague here in the math department, and he has recently been joined by Mikhail Khovanov who moved here from Davis. The relation of Khovanov’s new homology theory for knot invariants and the Heegard Floer theory is the subject of recent work by several mathematicians, including a second new Columbia faculty member, Ciprian Manolescu.

There’s a fantastic new set of introductory lectures on quantum field theory by Luis Alvarez-Gaume and Miguel Vazquez-Mozo. In less than a hundred pages they cover a wide range of subjects including the basics of quantum field theory, anomalies, renormalization, external field problems and supersymmetry. Page for page it’s by far the best introduction to the subject I’ve ever seen. For some other similarly excellent introductions to the subject, see one by ‘t Hooft and one by Pierre van Baal.

The last two items come from links on Gerard ‘t Hooft’s excellent web-site which includes a useful page on How to Become a Good Theoretical Physicist. He has just put up a new page on How to Become a Bad Theoretical Physicist, where he notes that “It is much easier to become a bad theoretical physicist than a good one.” This page is still under construction, I fear that he has a large amount of potential material for it.

Atiyah’s piece is very nice. It is very interesting that mathematicians’ connection to art is always made through beauty, harmony etc. Well,

art historians would tell you that these are

‘t Hooft says on his web page at http://www.phys.uu.nl/~thooft/theoristbad.html:

“… Young and inexperienced students could surf the web and get seriously confused by what they find. Therefore … Here is my BLACK LIST. …”.

My personal opinion is that “Young and inexperienced students” should be exposed to all kinds of stuff – right, wrong, crazy, sane, etc – so that they can form their own ability to judge stuff. Further, such concern about “Young and inexperienced students” is what led to the death of Socrates.

Tony Smith

http://www.valdostamuseum.org/hamsmith/

PS – Although I have not yet made ‘t Hooft’s BLACK LIST, ‘t Hooft goes on to say:

“… There are many more to add. I’ll be back when I found their names.

G. ‘t Hooft …”.

I’ve done almost everything on t’Hooft’s “good” list. This proves that I am a good theorist! Why didn’t I know this 20 yrs ago?

The primer on QFT was indeed very good, nice find.

-drl

No D R L, at best it proves that you SHOULD be a good theorist… π

I like Atiyah’s article as well…..to bad Jean-Paul didn’t finish.

If theory is the role of the architect, then such beautiful proofs are the role of the craftsman.Of course, as with the great renaissance artists, such roles are not mutually exclusive. A great cathedral has both structural impressiveness and delicate detail. A great mathematical theory should similarly be beautiful on both large and small scales.As the current story of the interaction between geometry and physics shows, the feedback from science to mathematics can be extremely profitable, and this is something I find doubly satisfying. Not only can we mathematicians be useful, but we can create works of art at the same time, partly inspired by the outside world.Mathematics: Art and Science

Impressive, and always lots to learn.

It’s always good to learn some history, as John Baez relates here

‘… Thereβs a fantastic new set of introductory lectures on quantum field theory by Luis Alvarez-Gaume and Miguel Vazquez-Mozo…’

Thanks for this link, Peter. I like the explanation on p71: ‘… we find the electromagnetic coupling grows with energy. This can be explained heuristically by remembering the effect of the polarisation of the vacuum … these virtual pairs behave as dipoles that, as in a dielectric medium, tend to screen this charge, decreasing its value at long distances (ie at lower energies).’

If so, then shouldn’t people be going all the way here, and developing a physical model of the polarised virtual field that will allow an alternative, more classical-type, calculation of the usual QED results, to avoid renormalisation? If only there was more of this heuristic explanation in physics, and less abject speculation (ST)…

Personally, I would have liked to see an introduction to non-perturbative aspects of QFT. I feel that students are sort of cheated by a purely perturbative approach. I thought that Luis A-G, more than almost anyone else, is qualified to write such an introduction.

When mathematicians start to talk about the beauty of their discipline they end up returning to a 19-th centurys classicistic discourse: cathedrals, Bach fugues, white marble…

sigh. I would wonder how indian or chinese mathematicians describe their discipline in aesthetic terms which conventional comparisons they use to describe their most inner feelings. Do japanese mathematicians compare proofs with cherry blossoms or do they find such comparisons as annoying then myself?It is quite amazing to know there is a how-to-be-a-good-theoretical-physicist recipe on t Hooft’s webpage. Then, can we massively produce the good theorectical physicists by his magic suggestions?

t Hooft provides necessary, but not sufficient conditions.

I would wonder how indian or chinese mathematicians describe their discipline in aesthetic terms which conventional comparisons they use to describe their most inner feelings.Maybe as a Taoist figure topological expressed Ying and Yang, defined, as a Calabi Yua?

Tony Smith, might have an answer for you?:)

On my speculation could General Relativity understood these “momentum occasions” as inclinations of circles and ellipses in martial art forms?:)

Last comment I will make like this Peter, as I know you like to run a tight ship.

I see that ks is exactly on the same track as what I was going to say.

The connection from mathematics to art is usualy made through beauty and harmony, using the pre-XIXth century concept of art.

Take music: The tonal harmonic system ended (I would say Mahler gave it a final blow) more or less at the same time as quantum mechanics was born, and it was replaced by atonal, dodecapohony etc. Are mathematicians ready for such a radical step? Can anybody tell me whether there was any radical change in mathematics methodology except for the same old proofs getting longer and longer?

Can anybody tell me whether there was any radical change in mathematics methodology except for the same old proofs getting longer and longer?Now what does this have to do with the math?

Such a comparison I would think, was from the perspective of the artist himself and , not the completion of the 10th, although attempts as seen were made to do this?

http://en.wikipedia.org/wiki/Gustav_Mahler#Symphonies

Any way, was it meant as, “the shift to new mathematics” and not the death of tonal qualities in relation to perspective views on “sound ” and views on the cosmo respectively? We know how this shift happened if held to Wayne Hu.

Would mathematicians concurr?

Did anyone read the Fermilab link? The peak luminosity is 1.41 x 10^30 (not 10^32 as reported in the blog). But still a record.

Actually the number was right:

141 x 10^30=1.41 x 10^32

On the assorted link front, we see this:

http://xxx.lanl.gov/abs/astro-ph/0507619

GR explains what NG can’t. No dark matter!

-drl

D R L:

You might want to look at this response to the paper you mentioned. Apparently, their metric and assumptions aren’t self-consistent:

http://arxiv.org/abs/astro-ph/0508377

The above link was slashdotted today for some reason. I knew it sounded too good to be true.

ali and blank,

The rebuttal paper is by no means convincing. The posited matter distribution is not at all unreasonable, nor is it the only possibility. The remarkable thing is, someone actually bothered to solve the equations instead of invoking yet another hand-waving argument. I’m sure we’ll see a “re-rebuttal” soon!

-drl

The idea that General Relativity provides only tiny corrections to Newtonian Gravity as far as galaxies are concerned is not a hand-waving argument, but a result from a well-developed expansion for an arbitrary source (e.g., see chapter 39 of Misner, Thorne, Wheeler). The expansion obviously doesn’t hold if there is a singular mass distribution, and perhaps singular mass distributions are reasonable.

The point is that it was not handwaving exercise to write off GR for galaxies.

The question is what the dark matter is, it could be mostly asteroids, comets, planets, small dim dwarf stars, or black holes. I’ve not seen any suggestion that most of the mass of a galaxy is dark matter to justify the rotation. You can’t justify having 10 or so times as much dark matter as visible star mass in a galaxy without massaging the model to fit the ‘critical density’ prediction… So the rest of the dark matter is then assumed to be in the intervening spaces as exotic particles, a nice ST-type untestable prediction.

Arun et. al, Copperstock and Tieu explicitly state

“The absolute value of z must be used to provide the proper reflection of the distribution for negative z. While this produces a discontinuity in Nz at z = 0, it is important to note that this has no physical consequence since Nz enters as a square in the density and Nz does not play a role in the equations of motion. Moreover, the metric itself is continuous. This is analogous to the Schwarzschild constant density sphere problem that leads to a discontinuity in metric derivative across the matter-vacuum interface in Schwarzschild coordinates. In principle, other coordinates could be found to render the metric and its first partial derivatives globally continuous but this would be counter-productive as it would unnecessarily complicate the mathematics. As in FRW, our co-moving coordinates simplify the analysis.”

where of course FRW means Friedmann-Roberston-Walker cosmology.

This IMO is conclusive. There must be something wrong with the rebutters’ Killing vector argument.

-drl

D.R. Lunsford, thanks for this analysis π

It should be fairly easy to decide.

The z-dependence of N is

N= exp(- k |z| ) , k is some constant

Now what is limit as y-> 0 of Integral( Nz^2 dz, { -y, + y ) )?

If the limit is 0 then Cooperstock has a point. If it is not zero,

then there is a delta function there, and that is the singular disk.

To the list of QFT notes, I would also add the tome Fields by Warren Siegel (hep-th/9912205).

I’ve recently added more stuff to my page in the hope of making t’Hooft’s bad list! (All publicity is good when you’re suppressed!) π

Re: mine of 8:18 AM, upon reflection, that is not a good way of looking for a density singularity.

See this on why Cooperstock et al. are wrong:

http://cosmicvariance.com/2005/10/04/most-exciting-discovery/#comment-4996

Arun,

See thread on SPR. Story is not over π

-drl

I see 5 messages on SPR and nothing new. What am I missing?

RE: art and science

Saw this on slashdot:

Art of Particle Physics

http://www.symmetrymagazine.org/cms/?pid=1000198

look at the pdf, as apparently, their is an error in the basic page