Gravity, BF, and DSR talk by Jerzy Kowalski-Glikman

Judging from past experience the recorded talk will probably be available in video.

Gravity, Constrained BF theories, and DSR - Jurek Kowalski-Glikman - 22/02/07 - 1:30 PM

So something to look for Thursday next week.
the announcement is here:
http://www.perimeterinstitute.ca/en/Scientific/Seminars/Quantum_Gravity/ [Broken]
http://www.perimeterinstitute.ca/in...ent&task=view&id=50&Itemid=83&lecture_id=4349

====quote====
PIRSA:07020016
Title: Gravity, Constrained BF theories, and DSR
Speaker(s): Jurek Kowalski-Glikman - University of Wroclaw
Abstract: In my talk I would like to show how: 1. One can construct gravity as a constrained BF theory; 2. One can couple particles to gravity in this formalism; and to explain why I believe that 3. All this is relevant for DSR program.
Date: 22/02/2007 - 1:30 pm
Series: Quantum Gravity
====endquote====
after the talk there may be some delay getting the recording online but after a while you look here
http://www.perimeterinstitute.ca/en/Scientific/Seminars/PIRSA/ [Broken]
and click on "catchup"


=============================

Another thing happening next week is a talk by Martin Bojowald Tuesday 20 February
http://relativity.phys.lsu.edu/ilqgs/
where the audio will be available and PDF lecture notes to follow along with
He will be giving his summary of the three-week workshop at KITP SantaBarbara that
he helped organize
The Quantum Nature of Spacetime Singularities

 

what a pity, not to be able to hear Jerzy's talk. I am glad to know about that rule though, so I won't be expecting it.

 

Oh my goodness yes! I am very interested.

DSR really stands for "DE SITTER RELATIVITY"

I think what he is talking about is arguably the most promising direction being explored today in quantum gravity research.


Look at Kowalski-Glikman's summary of his talk. What more can one ask, at this point, than this?

In my talk I would like to show how:

1. One can construct gravity as a constrained BF theory;

2. One can couple particles to gravity in this formalism;

and to explain why I believe that

3. All this is relevant for DSR program.

They should really move his talk to room #405. Jerzy rocks.

 

Instead of advising you to read certain papers let me just make sure that you know they exist. This will let you understand where I'm coming from if nothing else.

January 2005 paper of Freidel and Starodubtsev seemed like a glimmer at the end of the tunnel for me (and I think some others). It was the first time I read the magic words "MacDowell-Mansouri". Even locally you had to have 5D because the 4D local approximation wasnt flat.
(the universe doesnt need 5D but a local description of it does)

http://arxiv.org/abs/hep-th/0501191
Quantum gravity in terms of topological observables
Laurent Freidel, Artem Starodubtsev
19 pages

"We recast the action principle of four dimensional General Relativity so that it becomes amenable for perturbation theory which doesn't break general covariance. The coupling constant becomes dimensionless [itex](G_{Newton} \Lambda)[/itex] and extremely small 10^{-120}. We give an expression for the generating functional of perturbation theory. We show that the partition function of quantum General Relativity can be expressed as an expectation value of a certain topologically invariant observable. This sets up a framework in which quantum gravity can be studied perturbatively using the techniques of topological quantum field theory."

This was followed, after a long wait, by
http://arxiv.org/abs/gr-qc/0607014
Particles as Wilson lines of gravitational field
L. Freidel, J. Kowalski--Glikman, A. Starodubtsev
19 pages, to be published in Phys. Rev. D
Phys.Rev. D74 (2006) 084002

"Since the work of MacDowell-Mansouri it is well known that gravity can be written as a gauge theory for the de Sitter group. In this paper we consider the coupling of this theory to the simplest gauge invariant observables that is, Wilson lines. The dynamics of these Wilson lines is shown to reproduce exactly the dynamics of relativistic particles coupled to gravity, the gauge charges carried by Wilson lines being the mass and spin of the particles. Insertion of Wilson lines breaks in a controlled manner the diffeomorphism symmetry of the theory and the gauge degree of freedom are transmuted to particles degree of freedom."

Then there came a realization (and some additional intuition) from John Baez student Derek Wise.
It was clearly important to understand M-M gravity and the role of the de Sitter, Wise paper suggested that the right way to understand was in terms of Cartan geometry which I think basically means "warped tangent" geometry. (but this made a connection with DSR which is sometimes described in terms of a curved momentum space.)

http://arxiv.org/abs/gr-qc/0611154
MacDowell-Mansouri gravity and Cartan geometry
Derek K. Wise
34 pages, 5 figures

"The geometric content of the MacDowell-Mansouri formulation of general relativity is best understood in terms of Cartan geometry. In particular, Cartan geometry gives clear geometric meaning to the MacDowell-Mansouri trick of combining the Levi-Civita connection and coframe field, or soldering form, into a single physical field. The Cartan perspective allows us to view physical spacetime as tangentially approximated by an arbitrary homogeneous "model spacetime", including not only the flat Minkowski model, as is implicitly used in standard general relativity, but also de Sitter, anti de Sitter, or other models. A "Cartan connection" gives a prescription for parallel transport from one "tangent model spacetime" to another, along any path, giving a natural interpretation of the MacDowell-Mansouri connection as "rolling" the model spacetime along physical spacetime. I explain Cartan geometry, and "Cartan gauge theory", in which the gauge field is replaced by a Cartan connection. In particular, I discuss MacDowell-Mansouri gravity, as well as its recent reformulation in terms of BF theory, in the context of Cartan geometry."

BTW since Jerzy K-G is giving the talk, in case anyone looks up his papers on arxiv you don't get all of them if you say "kowalski-glikman"
to get others you have to use DOUBLE HYPHEN and say "kowalski--glikman".

this still does not get all the papers but it gets almost all. Others you can get just by saying "glikman" because in those he typed a space after the hyphen and signed "J. Kowalski - Glikman" and so naturally arxiv just sees the single last name Glikman after the space. We should all have hyphenated names so that search engines could be confused more often, making the world a better place.

 

Thanks, William. I didn't know you keep a blog---glad to see it.
I appreciate having your summary of Jerzy K-G's talk.

 

not all blogs have to be grandcentralstation
you already have reported on two interesting PI talks that the rest of us have no other window on (the Jacobson and the Jerzy K-G)
that's damn good. I wouldnt measure by how much you write.

 

Donnelly's blog on Kowalski-Glikman's talk was too good to miss pasting in here:

http://williamdonnelly.blogspot.com/2007/02/gravity-bf-theory-and-dsr.html [Broken]
===quote from "Uncommon Information" blog===
Thursday, February 22, 2007
Gravity, BF theory and DSR

Today I attended Perimeter Institute's quantum gravity seminar by Jurek Kowalski-Glikman. He talked about recent work based on trying to translate successes in understanding 2+1 quantum gravity to the 3+1 case. 2+1 gravity is much easier to work with than 3+1 because it's a topological theory - it just says spacetime is flat everywhere. The only thing interesting that happens is around punctures in the spacetime. It turns out these punctures have dynamics just like point particles. One can show that when two such particles interact their momenta don't add exactly; instead they obey a type of Deformed Special Relativity. This is pretty good news, now if only we could do it in 3+1.

3+1 gravity isn't topological, but in a sense it's close. Freidel and Starodubtsev [1] showed that you can write 3+1 GR as BF theory of SO(4,1) plus some additional terms that come from breaking the SO(4,1) symmetry. This theory has 3 free parameters: Newton's constant, the cosmological constant, and the Immirzi parameter. When the cosmological constant is set to zero, the theory turns back into BF theory. Since the cosmological constant appears to be very small, their idea is to use it as a parameter for perturbation theory around the well-understood BF theory.

One can also couple point particles to this theory just as in 2+1, and the dynamics of particles with mass and spin falls out. Just as in 4-dimensional BF theory, strings can be naturally coupled to the theory as well [2], although this possibility hasn't really been explored yet.

So that was the background, now for the new work. Kowalski-Glikman has started computing the perturbation expansion of the theory. Unfortunately this quickly leads to problems: if you expand just to first order in the cosmological constant you already get the Einstein equation. This sounds like it would be good news, but it really isn't. Perturbation theory is supposed to make life easier by making your theory easier to solve, so it doesn't help at all to be left with the equation you were trying to solve in the first place. It was suggested that something more interesting might happen at higher orders of perturbation, but these are apparently quite difficult and the expressions get messy. There's always the possibility that the quantum perturbation theory could be simpler, but that remains to be seen.

Unfortunately there was not much to be said about the connection to DSR. It was speculated that there could be some kind of dimensional reduction to the 2+1 case where DSR is known to hold. This might be possible, but I don't see it.

So what did I learn from this talk? Quantum gravity is just way harder in 4d than in 3d. While Freidel and Starodubtsev's formulation seems to allow the topological techniques to be imported into 3+1, the perturbation theory seems very tricky. I really wish there had been more to say about the connection to DSR. Since it arises in such a natural way from group-valued momenta 2+1 gravity, one would hope that a similar argument could be made in 3+1. At least I can rest assured that clever people are thinking about it.

[1] Quantum gravity in terms of topological observables
Laurent Freidel, Artem Starodubtsev
http://arxiv.org/abs/hep-th/0501191

[2] Exotic Statistics for Strings in 4d BF Theory
John C. Baez, Derek K. Wise, Alissa S. Crans
http://arxiv.org/abs/gr-qc/0603085

===endquote "Uncommon Information" blog===

 

as a rough oversimplification of the current QG situation
I see it as a time of CONVERGENCE
and I see two clusters or 'teams' of nonstring QG researchers kind of cohering.

the A team there is Ashtekar Penn State group including Bojowald, and also Thiemann

their strong point is they actually grind right through the cosmo singularity with a consistent deterministic model----that fits all the data as well as Gen Rel.

their strong point is that they have Quantum Cosmology, which WORKS as far as we can tell and is closely tied in with Thiemann's grid quantum gravity, which he calls "AQG" for "algebraic" QG. Ashtekar has a new dynamics in the symmetry reduced cases of cosmology he has studied, and all of them agree that there is a convergence of this with Thiemann's new dynamics.

another strong point is that Ashtekar's group at Penn State keeps doing computer runs of various versions of bounce cosmology.

the approach of the Ashtekar team is in a certain way pragmatic and adaptive----they tinker and evolve their models
=====================
the B team
The other cluster could be called the "DSR, BF, and spinfoam" people.

their disadvantage is they don't have a working version of Quantum Cosmology and they don't seem to be doing much computer work. So they look more theoretical and less nuts-bolts. Instinctively we all want QG to come to grips with the big bang and they aren't doing this. so it doesnt look as exciting on the surface. But their work is very interesting

This group has Laurent Freidel, Jerzy Kowalski-Glickman, Artem Starodubtsev, Derek Wise,....I wont try to make a complete list.

Basically they have MacDowell-Mansouri on their side, and Willem de Sitter, and Elie Cartan, and maybe John Baez (sometimes) and maybe two-groups----like the Poincaré two-group. They have a lot of great mathematics on their side. Maybe John Barrett and maybe Alain Connes.

The B team might come up with a good idea of what matter is, and how it grows up out of the same ground as space and time. they have a number of very interesting long-shot possibilities.

And they have DSR (which the A. team doesnt have) and DSR may turn out to make testable predictions----but see Bee Hossenfelder's latest paper just to sober you up :-)
=================
I need to make these oversimplified pictures sometimes, so things won't seem so complex.:-)
Where does Kirill Krasnov fit? or Lee Smolin's several initiatives? obviously it's not this simple.
Rovelli is more on the B team side, I think, because his latest work used spinfoam formalism---but it was also very pragmatically oriented towards gravitons and showing the correct semiclassical limit