Baratin and Freidel: a spin foam model of ordinary particle physics

marcus

Many of us are so eager to discuss categorics---a sign of how important it has become as a way of transforming how we view and understand mathematics these days. But actually part of the theme here is not explicitly involved with categories, as far as I know so far-----namely the BARATIN FREIDEL work on
Feynman graph spinfoams

which might turn out to involve categories explicitly but so far didnt AFAIK.

so as not to lose sight of the non-categoric side, I have highlighted parts of Francesca's post earlier in this thread :

Anyone is welcome to correct me if I am wrong, but to me it seems
that so far THERE NEVER HAS BEEN a background independent perspective on usual field theories

So far Feynman graphs have always been defined on a flat space or some setup curved space which is morally flat, but never defined in a background independent way (without reference to any background metric).

and the appliance gadget by which this is accomplished is a new thing, namely a Feynman graph spin foam
====================

I have two main questions that I am waiting for the answers----only time will tell about this:

will Baratin and Freidel be able to extend the results to 4D and if so, when will the paper appear? (the 3D paper was back in April)

supposing they are successful, and the 4D paper appears, then will it explicitly have a categories angle?

marcus

*... correct me if I am wrong, but to me it seems
that so far THERE NEVER HAS BEEN a background independent perspective on usual field theories*

So what prior field theories does this make obsolete? Or what prior field theories does this approach NOT make obsolete?

The gadget accomplishing this is a new thing, namely a Feynman graph spin foam.
It seems that Freidel et al have TAUGHT A FEYNMAN GRAPH TO LIE FLAT, in the dimension space they want, as one can teach a dog to sit when one says "SIT!"

the Freidel-trained Feynman graph can still adopt all possible postures and proportions, with legs all different lengths, except without being embedded it nevertheless knows how to assume only those positions that are appropriate to living in a particular space.
so it INTRINSICALLY has the right geometry. it is INATELY at home in the proper dimension.

that is what a "Feynman graph spinfoam" is, AFAICS. It is a Feynman graph that does not have to be embedded in some rented Minkowski apartment because it is has an instinctive sense of geometry.

Psssst! this means we don't need space any more.
========
Please let me know if you disagree with either the interpretation or the attributed significance.
disagreement would be welcome!

Kea

Oh, yes! Even if it looks a lot like the last one, secretly it is really categories through and through. One is really taking geometric realisations of n-functors into the representation (Poincare) category, philosophically like in TFTs. Recursive triangulations are secretly related to Street's oriental diagrams. Balls with marked points and their dual trees are just the sort of thing the operad people deal with...

...and so on.

marcus

but I will still be curious to see if it is explicitly categories or not.

we could bet.

I will bet that Baratin Freidel DO bring out their 4D paper sometime this year
and that it does indeed show how to rewrite Feynman graphs as spinfoams
(thus giving a background independent version of usual field theory)
BUT that there are no explicit categorics.

I hope you bet to the contrary, that there will be explicit categorics.

then I will win: W T !
===============

I think that they will still have to turn on gravity. Maybe that will require some twogroup construction.
If they succeed in the next paper that is still only describing the flat
G -> 0 limit of what the real theory has to be. It will have usual field theory, and thus matter, in a zero-gravity spinfoam world. And I bet not a word about categories. Shall we bet?

Kea

All right. I don't think there'll be much category theory, but I do think there will be a word or two. And I don't mind losing a bet to you, Marcus!

selfAdjoint

Thing about categories, which even their partisans grant makes skeptics smile, is that with sufficient skill and ingenuity you can do ANY math in categories, especially now that n-categories (recursive categorization) has/have been added to the tool kit. Categories can be to math as macros are to programming.

The perennial question about categories is not "Can we do this theory in categories?" but "Can categories give us answers to these questions that we couldn't get without categories?" (Never mind "easier"; that's in the eye of the beholder. Some people get off on down and dirty hard analysis; look at Hardy; his hobby was simplifying awful complicated integrals).

marcus

Pragmatic. proof of the pudding. Maybe my attitude is similar to yours. I also try to look at results, particularly does it make people SMARTER? if they use categorics part of the time, do they see analogies quicker? is their inventiveness speeded up?

it is a kind of "smart pills" (as in the expression "now you're taking smart pills") and using categorics seems to make some people frazzled or even wacky and some more creative. the result is not always good, but sometimes is.

In this regard I am only interested in research say since 2002 because only lately did I see it impinge on physics (in ways that are explicit and make sense to my limited perception). Maybe all categorics was useless to physics before that---I don't know about that.

but now I am beginning to see a correlation. the hidebound rejectionist attitude may be correlated with mediocrity and lack of inspiration. and some sense of "higher algebra" (whether categoric or some other) seems correlated to promising new physics ideas.

I am waiting to see---my attitude is "by their fruits ye shall know them". We will just see if the people who come up with the necessary new ideas are the people who are taking smart pills, or the others.

Probably trigonometry was not necessary. Hipparchus invented it around 140 BC roughly, and it was convenient but you PROBABLY COULD DO EVERYTHING just using geometry. nevertheless he made trig tables.
Probably Cartesian graph paper was not necessary. You probably could do everything with elaborate geometric constructions and not using plotted formulas. Probably some hidebound rejectionists were scoffing this. But Descartes went ahead and promoted his coordinate methods.
YOU CAN ALWAYS DO EVERYTHING THE OLD WAY. the question is whether the people using the new way appear to be more clever and do they invent the necessary things. and the question is do the people who reject the new way, do they seem mediocre and uninventive. Or is it different? I can only learn by watching the outcomes.

marcus

We have a bet, Dea Kea!
If they include a word or two of categorics then you win.
If they have no explicit mention of categorics then I win.

this is only if the paper comes out this year. if the problem proves unexpectedly intractible and they get stalled, bets are off.

I wish someone would speculate what the Baratin Freidel 4D case will look like. I can see how they construct a flat Feynman spinfoam in 3D spacetime. It is just a PARTITION FUNCTION that somehow remembers that it is supposed to dwell in 3D even without a surrounding 3D spacetime to remind it. Like one of those shape-remembering pieces of metal, that go *boink* and flip back to their imprintment.

Formally it is all seemingly straightforward, the trick is to get the right partition function. but spinfoams in 3D are regarded as somewhat rudimentary. maybe in the 4D case the partition function will be similar but just a bit gruesome.

Is that all, do you think? Will everything look like the 3D case except messier? I think I could stand that, at least if I had a chocolate malted milkshake to steady my nerves.

Careful

***
but now I am beginning to see a correlation. the hidebound rejectionist attitude may be correlated with mediocrity and lack of inspiration. and some sense of "higher algebra" (whether categoric or some other) seems correlated to promising new physics ideas.

I am waiting to see---my attitude is "by their fruits ye shall know them". We will just see if the people who come up with the necessary new ideas are the people who are taking smart pills, or the others.
***

So you say :
(a) 99,8 percent of physicists is unimaginative and more mediocre than category theorists
(b) you have to know category theory in order to be smarter

Moreover, there is only a hidebound rejectionist attitude when a large community accepts the use of the subject under consideration.

****
Probably Cartesian graph paper was not necessary. You probably could do everything with elaborate geometric constructions and not using plotted formulas. Probably some hidebound rejectionists were scoffing this. But Descartes went ahead and promoted his coordinate methods.
YOU CAN ALWAYS DO EVERYTHING THE OLD WAY. the question is whether the people using the new way appear to be more clever and do they invent the necessary things. and the question is do the people who reject the new way, do they seem mediocre and uninventive. Or is it different? I can only learn by watching the outcomes ***

This shows that you do not understand history. The method of Descartes was immediately recognized, just as special relativity, Maxwell theory and so on... . Instead of making erroneous political manifests you could contribute by explaining the useful, new insights for physics, as I asked you before.

Careful

Kea

Classic.

marcus

I think you meant classic blooper. Hope you did anyway.
My point was that historically there were some holdouts to the method of Descartes. Indeed there were lots! Newton for example.

Descartes explained his coordinates in 1637 (Discourse on Method, Geometry) and Newton's Principia appeared in 1687. Fifty years later. You can see him strictly avoiding Cartesian method. The example of Newton suggests that Cartesian coordinates WERE NOT FASHIONABLE at least in some circles even 50 years after exposition.

Here
http://members.tripod.com/~gravitee/booki2.htm
you can see Newton using Euclidean method to discuss circular motion in a plane, where we would today normally use Cartesian coordinates.

To make my point (the analogy with category theory) I only need to know that there were SOME holdouts
Cartesian coordinates are a good analogy to categorics. Even though they were available and would have been convenient, Newton made do with a pre-Cartesian approach. At least here in Book I section 2 and IIRC more generally. And unquestionably so did many others. Indeed 300 years later there were still people who strenuously avoided coordinates and preferred Euclid's methods. I knew one of them personally.
Newton of the Principia Book I was hardly the sole holdout, Greek style plane geometry still has class (it is classic after all).

What I am trying to say with this example, about categorics, is that one should not look for something that you CAN'T DO without the new method. There will often be some way to kludge around and make do, and that doesnt prove anything. It can even be a matter of taste. What one should look for is cases where someone GETS DIFFERENT IDEAS by solving the same problem by way of a different conceptual framework.

If anyone wants to see more of Newton Principia
http://members.tripod.com/~gravitee/toc.htm

Kea

What do I win, if I win?

Yes, classic blooper.

marcus

Well, I could write a (slightly disrespectful) rhyming poem about how wonderful you are.
Let me think about it. It probably wouldn't be a limerick. most likely a doggerel quatrain.
But I'm the one who is going to win! Can you write just-a-touch disrespectful light verse?
================
I wrote this next when out of sorts, before I saw your post:

I think we should just avoid or ignore complaining about category theory in this thread. People should use it if it gives them good ideas and inspires them to solve problems. And NOT use it if it DOESN'T.
People who don't get any good from it should simply not bother. After a point, more talking to them will not help them. In some way it seems silly to argue about the Goods and Bads of some (to an extent optional) mathematical method or framework, with someone with a mindset unsuited to it.
==============

From my viewpoint, Baez has already made abundantly clear to me as observer that it is a great source of new ways to look at things and that it is coming in to physics. Also Urs Schreiber is a bellweather in this respect. So I will be sure to keep my eye out for things happening with categorics and physics. I am also glad to see new stuff come out that does NOT use category theory. Whatever floats the researcher's boat.

So I will do what I can to ignore arguing about the merit of categorics, or lack thereof, and hope I succeed.

Careful

**I think you meant classic blooper. Hope you did anyway.
My point was that historically there were some holdouts to the method of Descartes. Indeed there were lots! Newton for example.**

This example is not even a counterexample to what I said. The method of descartes was for sure accepted by more than 0,2 percent of scientists.

By the way Marcus, for someone with a nonexpert opinion, you often refer to the notion of wrong/right mindset and to what is hopeful/sufficient evidence for something.

Careful

john baez

You win; I give up. In fact I gave up online debates some time ago.

For those who are interested:

Such models aren't what I'm talking about. I'm talking about how the category of Hilbert spaces (Hilb) and the category of n-dimensional cobordisms (nCob) are both monoidal categories with duals. The fact that Hilb has duals allows for quantum teleportation; the fact that nCob also has them is what allows you to straighten out a kink in a rope (in the case n = 1).

This is simply a fact, not a "model" - and certainly not a model where quantum entangled particles are connected in some way, e.g. by an "invisible rope". Quantum entanglement arises from the fact that Hilb is non-cartesian, unlike the category of sets. nCob is also non-cartesian.

(For a monoidal category to have duals, it must be non-cartesian, but not vice versa. Or, in physics speak: we need entangled states to carry out quantum teleportation, but we also need more. All this is nicely explained in Bob Coecke's paper on Kindergarten quantum mechanics.)

While these are just mathematical facts, they point the way towards models of quantum gravity, by showing us which class of mathematical structures combine the physically important features of general relativity and quantum mechanics.

But, we need to take another step or two - and probably many more we haven't seen yet. For starters, nCob is better thought of as a monoidal n-category with duals. This describes all the ways we can stick together small pieces of n-dimensional spacetime; it captures the n-dimensionality of spacetime in a way that a mere category can't do.

This suggests trying to define "nHilb" - an n-category of "n-Hilbert spaces" - and showing it's a monoidal n-category with duals. I did this for 2Hilb a while ago, and it turns out to be quite interesting. In particular: just as Hilb gives rise to Feynman diagrams, 2Hilb gives rise to "spin foams" - a 2-dimensional generalization of Feynman diagrams. If we went to nHilb for higher n, we'd get still higher-dimensiaonal diagrams.

I've never emphasized this aspect in my papers on spin foams, since I know most physicists don't like higher categories. But, I explain how it works in weeks 1-3 of the winter 2005 notes from my quantum gravity seminar.

A lot of work has been done on spin foam models by now, but they're still mysterious. For example, we've all heard a lot about the Barrett-Crane model, but it's still unclear why Simone Speziale and Dan Christensen are getting really good agreement with the graviton propagator based on calculations involving a single big 4-simplex, refinements of Carlo Rovelli's original calculation. They made a lot of progress on this last week: Dan's supercomputer calculations match what Simone is getting analytically. But why should these calculations work at all - after all, if any model like this is right, you'd expect spacetime to be made of lots of small 4-simplexes. Viqar Husain has some ideas....

And then there's the Crane-Sheppeard model. This explicitly uses infinite-dimensional 2-Hilbert spaces, namely representations of the Poincare 2-group. But what does it mean, physically? Is it related to Baratin and Freidel's spin foam model for ordinary quantum field theory on Minkowski spacetime? I guessed it was... but my students Jeff Morton and Derek Wise have been doing a bunch of calculations with Baratin and Freidel, and they seem to be concluding that it's not.

However, they found the Crane-Sheppeard model includes the Barrett-Crane model in a certain sneaky way. And, perhaps the best part is: Freidel now understands 2-Hilbert spaces and 2-groups, and he wants to keep studying models based on them!

marcus

I'll fetch some related links, in case something turns up or anyone is interested. I saw some recent papers by Speziale and also by Christensen and friends. UWO must be a good place to do computational quantum gravity, which ought to become important.


Here are some Christensen links. He is at Uni Western Ontario---part in QG-physics and part in math+computer science. They have supercomputer facilities. Wade Cherrington is a grad student there, and Josh Willis from Ashtekar's Penn State institute is a post doc. If it turns out to be possible to numerically simulate the quantum evolution of a world geometry by means spin foam then I suppose this might eventually happen on a UWO cluster.
http://arxiv.org/abs/gr-qc/0512004
http://arxiv.org/abs/gr-qc/0509080
http://arxiv.org/abs/gr-qc/0508088
==========

Here are some Speziale links
1. gr-qc/0606074
A semiclassical tetrahedron
Carlo Rovelli, Simone Speziale
10 pages

2. gr-qc/0605123
Towards the graviton from spinfoams: higher order corrections in the 3d toy model
Etera R. Livine, Simone Speziale, Joshua L. Willis
24 pages, many figures

3. gr-qc/0604044
Graviton propagator in loop quantum gravity
Eugenio Bianchi, Leonardo Modesto, Carlo Rovelli, Simone Speziale
41 pages, 6 figures

4. gr-qc/0512102
Towards the graviton from spinfoams: the 3d toy model
Simone Speziale
8 pages, 2 figures
Journal-ref: JHEP 0605 (2006) 039

5. gr-qc/0508106
On the perturbative expansion of a quantum field theory around a topological sector
Authors: Carlo Rovelli, Simone Speziale
7 pages

6. gr-qc/0508007
From 3-geometry transition amplitudes to graviton states
Authors: Federico Mattei, Carlo Rovelli (CPT), Simone Speziale, Massimo Testa
18 pages
Journal-ref: Nucl.Phys. B739 (2006) 234-253

Here is another interesting thing that turned up:

Kea will be glad to hear that.
Don't let me get in the way if someone wants to be reply to the general sense of JB's post, I am just assembling some detail to think about in that connection.

Sauron

Just an small sugestion.

In my opinion the programing analogue of cathegory theory would be UML (uniform modelling language). It is fine to plot diagrams and clarify flow of information. But you can do everything just implementing the apropiate class.

Returngin to the maintopic, i have just made a first (and complete) reading of arXiv:gr-qc/0607014.

To say it easy, I had readed the talks in other thread about de-sitter but the by far the part wich i understand less is the origin of the point lagrangian that they present in eq 3.1. I mean, it is basically the lagrangean of a classicla point particle carriying somehow information about so(3,1) álgebra or something similar? Wich sense makes that?

I see that they later show that it describes a particles with "all that good behaviours" but even so i don´t see clear that lagrangian (yeah, sure it is my fault).

And later, in chapter 5 when it makes a wilson loop with the exponential of that lagrangian, i simply don´t see the relation with the Feyman amplitudes. Maybe i need to read some previous papers? perhaps the ones aobut hidden quantum gravity in 3-d Feyman diagrams?