Renate Loll video lectures on quantum gravity (Perimeter Scholars series)

[marcus]

Lecture 1: http://pirsa.org/10010094/ (25 January)
Lecture 2: http://pirsa.org/10010095/ (26 January)
Lecture 3: http://pirsa.org/10010096/ (27 January)
Lecture 4: http://pirsa.org/10010097/ (28 January)

This is planned as a three-week series of one-hour lectures.

She does not use slides. She writes on the blackboard as she talks.
Lecture 1 gave the outline for the course. Loll is well-organized.

She plans to cover nonperturbative QG: Both the canonical (e.g. Loop) and the
covariant or path integral (e.g. triangulations) ways of doing nonpert. QG.
I just watched the first hour lecture. My impression is she has her act together
and the series will prove a valuable video resource.

 

[torquil]

My impression is she has her act together
and the series will prove a valuable video resource.

Agreed!

I skimmed through the the first 2.5, and watched the rest of the third one in detail. She has arrived at an expression for a graviton field operator, based on considerations about gravitational waves in linearized gravity. The lectures seem promising.

EDIT: Lecture 4 was mainly an introduction to second quantization, and introduction of path integrals.

Torquil

 

[Finbar]

Watched the first two. Will watch the third today.

They seem good. But as she points out its a hard subject to lecture.

 

[conway]

I watched the first one and found it to be pretty pointless. I wasn't going to watch any more but the topic of Lecture 4 piqued my interest. It seems her motivation was that she whipped through a bunch of material in Lecture 3 about gravitons and afterwards from the students questions she realized that they didn't understand the "basics" of second quantization. So she did a "review" of this in the first 15 minutes of Lecture 4. I have to say she didn't do all that bad a job of it except for the fact that she seemed really embarrassed about the fact that she was even doing it. I didn't think it was kid stuff.

Then she more or less derived the path integral formulation which I followed most of the way through with some lapses before losing her at the end. But I'm still going to ask one question about her closing comments, regarding how the effective contributions to the path are dominated by paths which are "nowhere differentiable". (I think I'm capturing the gist of what she said.) She elaborates by describing these paths as everywhere zigzagging.

My question is that in the complex domain (because she talks about integrating along paths in complex time) the definition of differentiability is very different from our intuition about smooth being equal to differentiable. All kinds of smooth functions in the complex domain are not "differentiable", only analytic ones are. For example, the function that stretches the complex domain as a rubber sheet mapping x to 2x and y to 3y is not "differentiable", but it is obviously smooth.

So my question is: is she making a mistake by describing the paths in question as somehow jagged?

 

[torquil]

My question is that in the complex domain (because she talks about integrating along paths in complex time) the definition of differentiability is very different from our intuition about smooth being equal to differentiable. All kinds of smooth functions in the complex domain are not "differentiable", only analytic ones are. For example, the function that stretches the complex domain as a rubber sheet mapping x to 2x and y to 3y is not "differentiable", but it is obviously smooth.

So my question is: is she making a mistake by describing the paths in question as somehow jagged?

I think I can add something to this: After the rotation, the path is still considered as a function of only one real variable, not a complex variable. This is despite the fact that the justification for the rotation is that the path is an analytic function in the complex plane of rotation, and something about the Lagrangian also being analytic there (I'm not sure).

So the differentiation in question is with regard to this real variable which determines the position on the imaginary axis, so it is differentiation in the "real sense". It corresponds to differentiating the value of the path's position with respect to the length along the imaginary axis.

Because of the assumption about the path being an analytic function, the derivatives along the imaginary axis and the real axis are related, right? Allthough this seems like a contradiction, since it cannot be analytic if it is nowhere differentiable in the real sense along the imaginary axis

Torquil

 

[Physics Monkey]

As torquil points out, one definitely should not think of any of the "typical" paths as analytic objects. They are jagged stochastic objects, continuous but nowhere differentiable in the real variable sense. For example, the "Wick rotation" or "analytic continuation" of the free particle path integral in quantum mechanics is formally identical to the problem of diffusion (where we reinterpret imaginary quantum mechanics time as real diffusion time). Here by diffusion I mean mathematical Brownian motion most rigorously described as a stochastic differential equation. This differential equation can be thought of as describing a random walk on a discrete lattice in a particular limit of vanishing step size and step time. You must take the limit of step size going to zero in such a way that the step size $$a$$ and step time $$\tau$$ satisfy $$a^2 /\tau \rightarrow \text{constant}$$. This formula is enough to see that the velocity $$v \sim a/\tau$$ is typically going to diverge in this limit.

The more sensible meaning of analytic continuation in these contexts comes from the correlation functions. These objects, formally defined using the path integral, should be analytic in their arguments (at least in some domain, depending on which correlation functions you study). This is the more rigorous meaning of analytic continuation in the path integral.

 

[marcus]

Lecture 1: http://pirsa.org/10010094/ (25 January)
Lecture 2: http://pirsa.org/10010095/ (26 January)
Lecture 3: http://pirsa.org/10010096/ (27 January)
Lecture 4: http://pirsa.org/10010097/ (28 January)
Lecture 5: http://pirsa.org/10010098/ (29 January)
Lecture 6: http://pirsa.org/10020060/ (1 February)
Lecture 7: http://pirsa.org/10020061/ (2 February)

Evidently planned as a three-week series of fifteen one-hour lectures, pitched at Masters student level, which I suppose might become the core of a textbook. (Basically an introduction to the main approaches in 4D quantum gravity research.) Have to look at Claus Kiefer's QG book to see if there is a niche for a Loll book.
Kiefer's Oxford monograph on QG came out in 2004 and costs about $175. The second edition appeared in 2007. Here's the TOC:

1: Why quantum gravity?
2: Covariant approaches to quantum gravity
3: Parameterised and relational systems
4: Hamiltonian formulation of general relativity
5: Quantum geometrodynamics
6: Canonical quantum gravity with connections and loops
7: Quantisation of black holes
8: Quantum cosmology
9: String theory
10: Quantum gravity and the interpretation of quantum theory
11: References

There could be a market niche. Loll's triangulations approach only became widely visible in 2004 when they got a result for 4D, and in 2005 when they showed dimensional reduction at small scale and the link to Asymptotic Safety. The field does look substantially different now in 2010. Loll is doing a really good job with these lectures and shows she has the command and communication chops to write a successful intro textbook to QG.

If anyone wants to check out Kiefer's book in more detail here is the OUP page:
http://www.oup.com/us/catalog/general/subject/Physics/QuantumPhysics/?view=usa&ci=9780198506874

 

[Finbar]

Watching the 6th lecture now. Its really interesting seeing how Renate thinks. It really gives good insight into CDT I think. Her explanation of good and bad gauge fixing conditions reminds me of the conditions she applies to the CDT path integral.

 

[atyy]

Is she still saying CDT and Asymptotic Safety go together? Or does it look like Horava now (http://arxiv.org/abs/0911.0401)?

 

[torquil]

Is she still saying CDT and Asymptotic Safety go together? Or does it look like Horava now (http://arxiv.org/abs/0911.0401)?

She hasn't gotten that far yet. I'm currently watching the Loll's Seventh now.

EDIT: I think something is wrong with the Flash video at 25m0s in the seventh lecture. Thankfully, there are other formats available.

Lecture 8 is all about repetition of symplectic/Hamiltonian dynamics with constraints.
Lecture 9 is about canonical formulation of gravity.

Torquil

 

[marcus]

Loll's 3-week course is now complete, and available video online.
Lecture 1: http://pirsa.org/10010094/ (25 January)
Lecture 2: http://pirsa.org/10010095/ (26 January)
Lecture 3: http://pirsa.org/10010096/ (27 January)
Lecture 4: http://pirsa.org/10010097/ (28 January)
Lecture 5: http://pirsa.org/10010098/ (29 January)
Lecture 6: http://pirsa.org/10020060/ (1 February)
Lecture 7: http://pirsa.org/10020061/ (2 February)
Lecture 8: http://pirsa.org/10020062/ (3 February)
Lecture 9: http://pirsa.org/10020063/ (4 February)
Lecture 10: http://pirsa.org/10020064/ (5 February)
Lecture 11: http://pirsa.org/10020065/ (8 February)
Lecture 12: http://pirsa.org/10020066/ (9 February)
Lecture 13: http://pirsa.org/10020067/ (10 February)
Lecture 14: http://pirsa.org/10020068/ (11 February)
Lecture 15: http://pirsa.org/10020069/ (12 February)

Incidentally, Prof. Jorge Pullin is currently teaching a one-semester introductory LQG course for undergrads. The second problem set is due 15 February, in a couple of days. Since there is no undergraduate-level textbook, the students are getting xerox write-ups of the lectures. Here is a brief course description and list of topics:
http://www.phys.lsu.edu/classes/spring2010/phys4750/
==quote==
PHYS 4750: Introduction to loop quantum gravity
...
This course will be an introduction for undergraduates to loop quantum gravity. To our knowledge, this is the first time such a course is offered in the world. We will assume minimal prerequisites: some knowledge of Lagrangian mechanics, some quantum mechanics and special relativity.

Topics:

1. Introduction: quantum gravity, why, what?
2. Special relativity and electromagnetism.
3. Some elements of general relativity.
4. Hamiltonian mechanics including constraints and fields.
5. Quantum mechanics and elements of quantum field theory.
6. Yang-Mills theories.
7. General relativity in terms of Ashtekar’s new variables.
8. Loop representation for general relativity.
9. An application: loop quantum cosmology.
10. Further developments.
11. Open issues and controversies.
==endquote==

 

[torquil]

Is she still saying CDT and Asymptotic Safety go together? Or does it look like Horava now (http://arxiv.org/abs/0911.0401)?

I have now watched all the lectures. She reached CDT in the last one. She didn't mention anything about asymptotic safety in that context, but did mention the results in the article you are quoting. I.e. the de Sitter limit and results for the spectral dimension.

Very nice lectures, I would say. A good introduction to a few different QG efforts.

Torquil

 

[alemsalem]

sorry to post here, but I'm being economic.
I'm watching the lectures now and I'm studying from Kiefer's QG book.
can I find problem sets that go along with these two??