Lectures on Loop Gravity (8 talks on the new version)

[marcus]

Today Rovelli started a series of 8 lectures on the new formulation of Loop Gravity

Here's the outline of the draft notes for Lectures on LG. It gives an entry-level introduction to the theory of spacetime geometry, for the students at the Zakopane school, as well as an idea of the essential math prerequisites.

http://arxiv.org/abs/1102.3660

I-Where are we in quantum gravity?

II-States and Operators

A-Elementary math: SU(2)
B-Elementary math: Graphs
C-Hilbert space
D-Operators
E-Spin network basis
F-Physical picture (this is one of the best sections IMHO)
G-Planck scale
H-Boundary states
​

III-Transition Amplitudes

A-Elementary math: SL(2,C)
B-Elementary math: 2-complexes
C-Transition amplitudes
D-Properties and comments

1. Superposition principle
2. Locality
3. Local Lorentz invariance​

IV-Derivations

A-Dynamics
B-Kinematics
C-Covariant lattice quantization
D-Polyhedral quantum geometry
​

V-Extracting Physics

A-Coherent states
B-Holomorphic representation
C-The euclidean theory
D-Expansions

1. Graph expansion
2. Vertex expansion
3. Large distance expansion​

E-What has already been completed

1. n-point functions
2. Cosmology​

VI-Conclusion

Appendix A: Open problems (1 - 17)

Appendix B: Alternative expressions for the amplitude

1. Single equation
2. Feynman rules
3. Using Y explicitly
4. Spin-intertwiner basis
5. Variants in the amplitude​

The talks are scheduled in hour segments: two on each of four consecutive days. A lot of credit for the Zakopane school (and the rapid progress in QG since 2007) goes to the ESF (European Science Foundation) and its QG funding network guided by John Barrett of Nottingham University and Hermann Nicolai of the Potsdam AEI. It's not an exaggeration to say that Barrett and Nicolai have shown exceptional leadership and (in particular) vision. Their vision seems to be paying off.

 

[marcus]

I just learned today that an update of "Lectures" was posted on arxiv over the weekend--so I printed it out and am reading through it.

There's additional material now, including problems---exercises for the student to work. Many or most sections seem to have problems inserted in them to help the reader see if he or she understands that section.

The revised edition has the same URL as before:
http://arxiv.org/abs/1102.3660

 

[marcus]

Website for the Zakopane QG school, currently in session.
http://www.fuw.edu.pl/~kostecki/school3/
107 participants listed, talks aimed at advanced PhD student and postdoc level

Funded by the ESF, QG network (quantum geometry and quantum gravity).
If you look at the list of talks you see a variety of approaches (for instance NCG, GFT, QFT on curved geometry...) besides Loop.

Here are abstracts from the school program describing two series of lecture:

Hanno Sahlmann/Kristina Giesel - Loop quantum gravity (series of 10 one-hour talks)

"The field of loop quantum gravity is the technically highest developed construction in quantum gravity. As in the last two schools there will be a thorough introduction into the underlying ideas and mathematical methods. The lectures will cover the basic construction of the kinematical hilbert space and some simple operators, working up to the dynamical Hilbert spaces and physical Hamiltonians following from the deparametrization models."

Carlo Rovelli - Spin foams (series 8 one-hour talks)

"The most active field in the network in the last years has been spin foam models, starting with the development of the graviton propagator and the new models, to coherent state techniques and recent asymptotic results, the generalisation to arbitrary 2-complexes and cosmological applications. The lectures will present the current perspective on the construction of these models in terms of 2-complexes."

 

[martinbn]

Will notes and/or videos from Zakopane be available? Sorry if that is on the website, i didn't see it.

 

[marcus]

Will notes and/or videos from Zakopane be available? Sorry if that is on the website, i didn't see it.

My guess is not, Martin. In fact, though I do not know for sure, and have seen no information about that, I feel fairly sure they will not be.
I'd be thankful to be proven wrong about that!

However it is possible to learn a certain amount from the "Zakopane Lectures" paper on arxiv.

It now has some "homework problems" interspersed, as you've perhaps noticed, and I think one of the problems was actually contributed by Roger Penrose! (An unidentified Roger is thanked.)

 

[martinbn]

Thanks, Marcus. I took a look at the paper on the arxiv but haven't read it carefully yet. I was hoping the talks at Zakopane had more detail. The review articles, that you give links to, seem very good, but the style is a bit difficult for me as a non-physicist. It would be nice if some of the people who attend scaned their notes.

When you say you are fairly sure that they will not, is it because you think (know) that they will appear in a book/proceedings?

 

[marcus]

...
When you say you are fairly sure that they will not, is it because you think (know) that they will appear in a book/proceedings?

Martin, you are right that the review articles need filling out with detail. They are not pedagoical.
Actually the first pedagogical article from Rovelli in a long time is this February 2011 paper called "Zakopane Lectures" http://arxiv.org/abs/1102.3660

And that you will probably find very frustrating because the math prerequisites are extremely condensed and pitched at advanced physcs grad student level!

But it is pedagogical---it has "homework problems" and tries to define things so it is reasonably selfcontained. It is pedagogical but at the "wrong" level: at a grad student level.

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

I have no inside track to the information. Basically I just have what is online----and past experience---to go on. My expectations are based on what I remember from past qg schools.

Correct me if I'm wrong but I don't recall slides PDF or video or anything coming out of the SECOND QG school, which was on the island of Corfu. There was some stuff from a few other people, but Rovelli's slides were not posted online

And I don't recall much useful stuff being posted from the FIRST QG school which was at Zakopane in 2007.

But if you go back and check it out and find that there are PDF slide sets for some of the key lecture series, please tell me!

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

So to respond directly to your question, I don't have any definite information about a book or about proceedings, and I haven't seen any indication that there will be any online resources coming from this year's Zakopane school.

what I wish would happen is that somebody would expand the *Lectures* and provide supplemental material.
I like the *new* Loop gravity a lot. but it is only about one year old. It emerged in early 2010. Potentially it is easier to learn than the old LQG formulation. Less excess baggage. More mathematically streamlined. But there hasn't been time yet for pedagogical material to accumulate.

The situation in that regard is inherently frustrating. I almost wish I had gone this week to Zakopane myself. Tuition and room accomodation are actually not very expensive (but it is a long way from where I live.)

 

[marcus]

... I was hoping the talks at Zakopane had more detail. The review articles, that you give links to, seem very good, but the style is a bit difficult for me as a non-physicist...

Martin I just realized you have a PhD in mathematics, so I understand this in a different light now! My previous reply to you was not exactly to the point. Sorry

There are parts of *Lectures* which could be obscure to a mathematician simply because physicists slenderize their notation---they use odd tricks to make writing more convenient.
We can do something about that, especially if you will help by pointing to obscure passages and notation, and help me puzzle them out.

I'll get some examples. What I have in mind is a kind of "Rosetta Stone" approach where we match up mathematician hieratic to physicist demotic.αβγδεζηθικλμνξοπρσςτυφχψωΓΔΘΛΞΠΣΦΨΩ∏∑∫∂√±←↓→↑↔~≈≠≡≤≥½∞⇐⇑⇒⇓⇔∴∈∃ℝℤℕℂ⋅

 

[marcus]

Here is a simple example of what I mean---too trivial to mention perhaps. On page 3 between equations (15) and (16) discussing lattice gauge theory, Rovelli writes a state as
ψ(h_l)

That could make it look as if the argument of ψ is a single group element. But one quickly realizes that it's not. ψ is actually defined on L-tuples of group elements, or indexed sets of them
(h₁, h₂, ..., h_L)
It is defined on a complete assignment of a group element to each link in the graph.

If I remember right, there is some other expository article that puts in curly brackets as a reminder of this, writing the state as ψ({h_l})
Whether or not this is a good idea, at least that way the casual reader will realize at once that he should think of a whole set of group elements, indexed by links---an assignment of group elements to links. The reader will not think that the state is defined on a single group element, so there is no initial moment of confusion.

I shouldn't make too much of this, it's trivial, but this is the kind of thing. The notation is compromised in order to make it lighter and easier on the eye.

I would like it if we could collect several examples of possible confusion happening in *Lectures*.

Here is another example, perhaps not as trivial. Look on page 5 at the top of the second column. He says that he will use the same symbol v_n to stand for a basis of intertwiners, and for an individual intertwiner, and for the corresponding eigenvalue.
This means that the symbol v_n plays several roles.
Correct me if I am wrong.
We could sort this kind of thing out and perhaps learn something in the process. It should be easy to do.

αβγδεζηθικλμνξοπρσςτυφχψωΓΔΘΛΞΠΣΦΨΩ∏∑∫∂√±←↓→↑↔~≈≠≡≤≥½∞⇐⇑⇒⇓⇔∴∈∃ℝℤℕℂ⋅

 

[martinbn]

Yes, Marcus, this is precisely my difficulty. Your first example is a good example. Although it is trivial it caused me to pause and think about it for a moment until I realized what it was.

I have to read more into the paper before I can say what troubles me. Of course it need not be the same thing for other people. May be in a couple of days, if I get to read the paper, I can start a tread with points I need clarification about. I am a bit concerned that they me be too elementary and clear to everyone but me, so I don't really want to bother people with it.

 

[marcus]

... I am a bit concerned that they me be too elementary and clear to everyone but me, so I don't really want to bother people with it.

That's often an unwarranted concern that one just has to get over. In a situation like this discussion board, if you sort things out simply and methodically, you can never tell who will be helped.

You are welcome to use this thread, as long as your focus is on the topic paper, "Zakopane Lectures", for whatever purpose. But you can of course start your own, either way is fine with me.

I wonder how it would look, and read, if we put in some curly brackets and such-like augmented notation, to make it more immediately understandable to non-physicist mathematicians. Would it start to look "heavy" or "overdressed"?

 

[marcus]

Will notes and/or videos from Zakopane be available? ...

Not videos so far (and I don't expect them).
But I was wrong about slides/whiteboard snapshots. I did not expect those to be posted but today I see some up at the QG school site:
http://www.fuw.edu.pl/~kostecki/school3/

EDIT the snapshots could be from a freehand transparency overhead projector, not whiteboard

Another afterthought. In the Loop Gravty *Lectures* on page 4 there is nice physics intuition problem contributed by an unidentified "Roger", who is thanked. I wonder if that could be Roger Picken. At first I thought it might have been Penrose, I don't know of very many Rogers in the qg business. But both of them are, to some extent, so that remains a mystery.

 

[martinbn]

Not videos so far (and I don't expect them).
But I was wrong about slides/whiteboard snapshots. I did not expect those to be posted but today I see some up at the QG school site:
http://www.fuw.edu.pl/~kostecki/school3/

Thanks, that's great. I was going to check later just in case, but they already have some on.

 

[marcus]

What I'm finding helpful is the Ashtekar slides and the Brunnemann notes/slides.
Because Rovelli's talk was already carefully laid out in the arxiv paper.
Brunnemann is talking about a critical issue, the volume operator. He has a way of calculating it and of resolving previous ambiguity.
Here are handwritten notes:
http://www.fuw.edu.pl/~kostecki/school3/pdf/Brunnemann.pdf
Here are slides:
http://www.fuw.edu.pl/~kostecki/school3/pdf/Brunnemann_volume.pdf