Clear concise Loop survey as of January 2012

[marcus]

...indicate that neither he nor KKL knew at first that the formulation was the same (p3): "The expression (3) was found independently and developed during the last few years by a number of research groups [15-21], using different path and different formalisms (and a variety of notations). Different definitions have later been recognized to be equivalent."

I just got back from supper and saw your post. This is pretty persuasive. I'll have to think about it.
Probably in the introduction to Zako Lectures Rovelli should have used some modifier. All the formulations are closely related and certainly one could say "essentially equivalent"
or "effectively the same but formulated in a variety of ways." I don't understand the actual situation well enough to guess what a more careful wording might have been.

 

[tom.stoer]

I think Marcus and Tom should stop arguing on this point; I think the argument is being done in good faith, but fundamentally you're going to disagree. I think (but probably wrong) that Tom is concerned with the intellectual aesthetics of the theory, which is pretty much defined by how it connects with other known theoretical ideas; marcus is solely focusing on the question of "correctness" with respect to nature --- these points of view both have merit, but I think it's going to be bizarre if some people on a forum will hash it out rather than, say, Rovelli et al.

In an attempt to bring the conversation back to the original point a little: marcus has been impressed by the loop *classical* gravity work; personally I was impressed too, until I thought a little harder about it --- now I'm not so sure; it may have bearing on the issue of a Hamiltonian. The problem is the lack of dynamics as proposed by Friedel et al. I'm satisfied that they have a good formulation of discretised gravity degrees of freedom, but I'm not sure that they have the correct *phase space*, since phase space is by definition the space of trajectories. For instance, I'm not sure how they will deal with inevitable graph changing operations --- I can't think of any way to make that consistent purely classically. In other words, I'm not sure (and in fact am very sceptical) that one can simply commute "discretisation" and "quantisation".

Good points!

I agree with you
a) technically b/c you seem to be inline with my reasoning regarding dynamics, Hamiltonian, phase space, interchaging discretisation and quantisation, ...
b) the rather bizarre case here in this Forum; I am convinced that we can trust in all the real experts who are not only clever enough to realize the weak points of the theory, but who are certainly smart enough to figure out the answers ...
c) regarding stopping the discussion b/c everything has been expressed and explained many times

 

[atyy]

In other words, I'm not sure (and in fact am very sceptical) that one can simply commute "discretisation" and "quantisation".

I agree with you
a) technically b/c you seem to be inline with my reasoning regarding dynamics, Hamiltonian, phase space, interchaging discretisation and quantisation, ...

Is the issue of interchanging discretization and quantization the same as asking whether in Rovelli's Zakopane lectures, the figure on p21 exists? There he indicates one should get from full QG to classical GR by j→∞, or by first discretization, then j→∞, then a continuum limit.

This seems to be the issue on the last slides of Ziprick's talk, and that Freidel makes in the long discussion following. Ziprick's last slide is too terse, and one has to listen to the conversation between Smolin and Freidel at 42:46 - 44:00 to understand the slide.

 

[marcus]

The FGZ paper ("loop classical gravity") and Ziprick's online video presentation of it are definitely key things for us to assimilate. Atyy it's great to have your reactions, to Ziprick's talk! (And the remarkable discussion following it. )

Freidel already has a followup paper, or one that I at least found to be exploring in the same groove. It focuses on the alternative ways to formulate classical GR. In particular the thinking surrounding BF theory and the different ways to get GR out of it (Plebanski, McDowell-Mansouri, Peldan-Jacobson-Bengtsson, Krasnov...)

This is by Freidel and Speziale
http://arxiv.org/abs/1201.4247
On the relations between gravity and BF theories
Laurent Freidel, Simone Speziale
(Submitted on 20 Jan 2012)
We review, in the light of recent developments, the existing relations between gravity and topological BF theories at the classical level. We include the Plebanski action in both self-dual and non-chiral formulations, their generalizations, and the MacDowell-Mansouri action.
Comments: 16 pages. Invited review for SIGMA Special Issue "Loop Quantum Gravity and Cosmology"

SIGMA is an online refereed journal which is gradually assembling a "special issue" or collection of articles on Loop gravity. Freidel Speziale and a number of other articles have appeared that have not yet been reviewed and formatted by the editors, so are not yet included in the "special issue" collection. But it's potentially a useful source.
Here is the SIGMA special collection of articles on Loop gravity/cosmology:
http://www.emis.de/journals/SIGMA/LQGC.html (Berlin site)
http://www.emis.ams.org/journals/SIGMA/LQGC.html (American Mathematical Society site)

 

[marcus]

Remember that the FGZ paper came out four months ago, in October. Freidel has been very productive in the days since then--three papers in January 2012 alone.
The Freidel Speziale paper I mentioned can supplement the discussion at Ziprick's talk and help to give us a handle on current thinking.

Here is the summary or "outlook" section at the end:

6 Outlook
One of the key difficulties with general relativity is the high non-linearity of its field equations. This complexity is enhanced further in the Einstein-Hilbert action principle, which is non-polynomial in the fundamental field, the metric. To obtain a polynomial action, one has to expand the metric around a fixed background. Then the perturbations can be quantized, but the theory is not renormalizable. An important line of research in quantum gravity imputes this failure to the background-dependent, perturbative methods, and seeks a background-independent formulation. When seeking for alternative approaches, the use of different fundamental variables with simpler actions is a useful guiding principle. In this respect, the relation of general relativity with BF theory appears very promising. The work appeared so far in the literature has unraveled the deepest level of such a classical relation, and introduced new tools and ideas to push forward the investigation of gravity in these variables. These results can be of benefit to approaches such as loop quantum gravity and spin foam models.​

In this thread we're trying to get an up-to-the minute picture of where Loop gravity research is and where it's going.

For newcomers who want to look at what is being discussed:

Google "ashtekar introduction 2012" and get http://arxiv.org/pdf/1201.4598.pdf

Google "rovelli zakopane" and get http://arxiv.org/abs/1102.3660

Google "freidel geiller ziprick" and get http://arxiv.org/abs/1110.4833

Google "jonathan ziprick pirsa" and get video http://pirsa.org/12020096

Google "freidel speziale BF" and get http://arxiv.org/abs/1201.4247