Rovelli's talk at Perimeter 4/4/12: video online, comment?

[marcus]

http://pirsa.org/12040059
Fine presentation today, room packed, good questions from audience (esp. from Turok but also from others.)

Rovelli will spend several weeks at Perimeter during which time he also makes a side trip to Princeton Institute for Advanced Study to give a slightly different talk:

http://www.princeton.edu/physics/events/viewevent.xml?id=347
High Energy Theory Seminar - IAS - Carlo Rovelli, Aix-Marseille University, France
Loop quantum Gravity: Recent Results and Open Problems
Description: The loop approach to quantum gravity has developed considerably during the last few years, especially in its covariant ('spinfoam') version. I present the current definition of the theory and the results that have been proven. I discuss what I think is still missing towards of the goal of defining a consistent tentative quantum field theory genuinely background independent and having general relativity as classical limit.
Location: Bloomberg Lecture Hall
Date/Time: 04/23/12 at 2:30 - 3:30 pm

He will also be giving a series of lectures on QG at the University of Vienna during the first week of September:
http://www.coqus.at/events/summerschool2012/

 

[genneth]

Very interesting. The thing which is new (in that one had to read between the lines rather than hear him say in papers) is that essentially commuting the classical and continuum limit is currently tricky, if not outright unknown. I think this is essentially the problem that Tom has been drawing our attention to, in the form of properly (whatever that might mean) quantising the constraints in the canonical formalism. Whilst I completely agree with the sentiment, I personally (betraying my roots in condensed matter) think that the proof will be in the eating of the pudding --- I think that before we have the necessary mathematics to properly quantise those constraints we will find by pure computation and comparison with experiment whether the theory as written is viable (not withstanding all the recent excitement about perhaps needing to restrict the type of triangulation allowed in order to get the right bit of the state sum).

Summarising: very nice talk with honest appraisal of the state of play --- something which can be hard to glean from papers.

 

[atyy]

Very interesting. The thing which is new (in that one had to read between the lines rather than hear him say in papers) is that essentially commuting the classical and continuum limit is currently tricky, if not outright unknown. I think this is essentially the problem that Tom has been drawing our attention to, in the form of properly (whatever that might mean) quantising the constraints in the canonical formalism.

Here's a paper which has a very brief discussion about it:
http://arxiv.org/abs/0809.2280
"In a sense, one needs that the large spin limit and the integration over the spins commute with each other. Whether this happens or not is not obvious: one might be worried, for instance, that the summation over spins is much less restricted than a summation over discrete geometries and that this will lead to stronger equations of motions. It might be, on the other hand, that the exponential suppression of non Regge–like configurations is strong enough to effectively reduce the summation to a sum over geometries. This is an important question that deserves to be studied further."

I think the FGZ paper is somehow related, but am not sure.

 

[marcus]

... Whilst I completely agree with the sentiment, I personally (betraying my roots in condensed matter) think that the proof will be in the eating of the pudding --- I think that before we have the necessary mathematics to properly quantise those constraints we will find by pure computation and comparison with experiment whether the theory as written is viable ...

Yes and yes! While I too share the sentiment that all should be done properly (whatever that means), I also think, as you say, that the primary test of whether the theory as written is viable will probably be empirical. "The proof of the pudding is in the eating."

It's nevertheless interesting to watch the struggle around that rectangular diagram, to get from the lower left corner to the upper right, involving two kinds of limits. At the moment my attention is focused on the Warsaw group's proposal (SN-diagrams) to make systematic the process of summing amplitudes of spinfoams up to a certain level of complexity---a number N of vertices.

I hope that proposal can be implemented as a computer algorithm. It seems to give a way to systematically generate all the spinfoam histories up to a certain complexity "cutoff" level (of course just those histories bounded by a certain spin network giving initial and final state information.) To me that seems like part of empirically "proving the pudding". Have the computer calculate and sum transition amplitudes up to some N. Then increase N, and see. I think you understand even more clearly the kind of thing I have in mind.

If anyone else is reading and is curious about this, google "puchta feynman arxiv" to get the Warsaw group's spinfoam feynman diagrams paper. In any case thanks both Atyy and Genneth for comments. I had to be out this evening so could not reply until now, which is past midnight here. Let's see how it looks in the morning.

 

[marcus]

Let's look at the PDF slides for Rovelli's talk and identify a few important ones.
There are 49 slides. The most important is surely going to be #19, but there will be a few others (e.g. #9) to mention as well.

Slide #19 is the rectangle diagram titled The general structure of a parametrized (general covariant) quantum theory.

Quantum theory                                              Classical theory
Transition amplitude           hbar→0                   Hamilton function
W(x,x')                                                          S(x,x')

∞                                                                 ∞
↑                                                                  ↑
N                                                                  N

Discretised                                                     Discretised 
quantum theory              hbar→0                      classical theory
W[SUB]N[/SUB](x,x')                                                        S[SUB]N[/SUB](x,x')

The horizontal left to right limit is taken as hbar→0, the usual classical limit.
The vertical upwards limit is taken as N, the number of steps or more generally the complexity of the discretisation, goes to infinity. Since there is no prior metric, there can be no idea of a "lattice scale" to shrink to zero. But one can, for example let N→∞ where N is the simply the number of vertices in foam histories contained in a given spin network boundary result.

In Rovelli's case, the lower right corner of the quad is REGGE CALCULUS and that path from Loop to GR does seem workable. Indications are the classical limit of Loop_N (lower left) is Regge (lower right) for fixed finite discretisation cutoff N, although that can still be argued about. And then the upwards limit from Regge to GR, as N→∞, takes you the rest of the way.

But we'd like more than that. We'd like it to be clear that you can start in lower left with Loop_N and let N→∞ and run straight up to a nice finite well-defined limit theory Loop at the upper left corner of the quad. With no limit, then, on how complex the spinfoam histories can be.

Personally I would not mind seeing that explored numerically in several cases, by machine.
The Warsaw group seems to be examining prospects of a computable algorithm that would let N be systematically increased. Both Rideout and Christensen have each applied heavy duty cluster computing to this kind of thing. I wonder if something analogous will happen in this case. My private sense is the Warsaw algorithm is ingenious and *deserves* to be run. We'll see.

 

[atyy]

I haven't had time to watch the whole thing - does Rovelli say anything about the Rovelli-Smerlak proposal to take the continuum limit (summing = refining)?

 

[genneth]

I haven't had time to watch the whole thing - does Rovelli say anything about the Rovelli-Smerlak proposal to take the continuum limit (summing = refining)?

Arguably the whole talk is based around it. The way Rovelli puts it is that in a generally covariant theory the discretised version reaches the continuum by just increasing the number of sampling points without a need to tune any parameters. This is in distinction to lattice QCD, for example.

 

[marcus]

I haven't had time to watch the whole thing...

It's tough not having time to watch an hour lecture. Demands on my time change from week to week and fortunately right now are light, but I know what you mean.

If anyone else has the time right now there's a related hour lecture that R. gave that morning which is meant to serve as a supplement (with additional examples and detail about the Hamilton function and mechanics without treating time specially.)

He tells the students they can treat the morning talk as "part of" the colloquium.
The relevant lecture is number 3 in what will probably turn out to be a series of 12 lectures--
four a week for three weeks or so, starting 2 April.

http://pirsa.org/C12012

Perimeter has these 3-week or so courses, the eleventh one they started this year would I guess be C12011.
R.'s is the twelfth course they started this year so it is C12012. I'm guessing that this one is just Mon-Thu, with a Fri-Sun break. We'll see. Anyway the morning talk for the dozen-or-so students on 4 April was a considerable help to understand the afternoon 4 April colloquium.

The individual URL for that day's morning talk is http://pirsa.org/12040021/ but you don't really need that if you have the C12012 URL for the whole three(?) week course series.

Bianca Dittrich was in the audience at the colloquium.

 

[atyy]

Arguably the whole talk is based around it. The way Rovelli puts it is that in a generally covariant theory the discretised version reaches the continuum by just increasing the number of sampling points without a need to tune any parameters. This is in distinction to lattice QCD, for example.

Did he say anything about the existence of such a limit? I think most people thought the Rovelli Smerlak limit didn't exist, and was actually divergent.

 

[genneth]

Did he say anything about the existence of such a limit? I think most people thought the Rovelli Smerlak limit didn't exist, and was actually divergent.

Yes, at the end, as one of the open problems --- he considers it a question of well-behaveness of radiative corrections. To be concrete, the system he really has in mind is the q-deformed version with a cosmological constant, which makes the sum obviously finite (the representations are bounded from above as well as below). His phrasing of the problem is then that of whether the N-vertex expansion is a useful one, i.e. does the first few terms really provide a good approximation to the full theory.

 

[marcus]

... To be concrete, the system he really has in mind is the q-deformed version with a cosmological constant, which makes the sum obviously finite (the representations are bounded from above as well as below)...

You could be right. I didn't hear any explicit mention of that q-deformed version, with positive cosmo constant. But it would make sense. I may have missed something and should listen to the talk again. I like what you say here:

*His phrasing of the problem is then that of whether the N-vertex expansion is a useful one, i.e. does the first few terms really provide a good approximation to the full theory.*

This seems like a good way to put it. For instance, restrict to the N=1 case (as I recall a Lewandowski et al paper does) and see what you get. With just one internal spinfoam vertex. And simple S³ geometries for initial and final.

Or pick some other finite N as limit of the number of internal vertices, and repeat what you did for N=1. Frank Hellmann's thesis was along these lines---I forget the details, like what N was. Lewandowski seems to be a leader in equipping for this research direction. Jack Puchta gave a ILQGS talk on it.

As I recall they already have some interesting results for very basic cases. So we'll see: is it useful?

======EDIT to reply to next post======
Genneth thanks for catching that!

It's not in the slides, but his (spoken) words refer to it. In addition, when discussing the finiteness issue, he clearly states (but again, only spoken) that it is UV finite always but only IR finite if one takes the q-deformed version.

A potential snag with the non-q-deformed version might be that it is difficult to say what UV vs IR limit really means -- precisely because it is just refinement either way. Nevertheless, I hope it is obvious (which probably means it is not) that the deformed theory is simply finite for any finite boundary state.

I just listened to the whole talk (not including questions at the end) and heard the points you mentioned. Right now I don't have anything to add to your post #12, so will not spend a post simply to say Amen.

 

[genneth]

You could be right. I didn't hear any explicit mention of that q-deformed version, with positive cosmo constant. But it would make sense. I may have missed something and should listen to the talk again.

It's not in the slides, but his (spoken) words refer to it. In addition, when discussing the finiteness issue, he clearly states (but again, only spoken) that it is UV finite always but only IR finite if one takes the q-deformed version.

A potential snag with the non-q-deformed version might be that it is difficult to say what UV vs IR limit really means -- precisely because it is just refinement either way. Nevertheless, I hope it is obvious (which probably means it is not) that the deformed theory is simply finite for any finite boundary state.

 

[marcus]

I can see I'm going to have to get to know Pirsa 12040059 better and also the paper that is closest to it in concept and content: Arxiv 1108.0832
The paper paralleling the talk is On the Structure of a Background Independent Quantum Theory

It has the quadrangle diagram that I copied in post #5, which is slide #19 of the talk. It's Table I of "On the Structure"

And it also has, as its table II, the corresponding diagram that you get when the concepts are applied to a CELL COMPLEX C, and you take the limit in the sense of nets, since cell complexes form a directed set. (This is common enough as mathematics but may not be familiar to everybody.) This appears a half-dozen times in the talk, as slides #26, #30, #34, #39, #43, #44, ... and more. This quadrangle diagram comes under the heading General Structure of Quantum Gravity--see slide #48:

Exact quantum gravity                                   General Relativity
transition amplitudes           hbar→0                Hamilton function
W(h[SUB]l[/SUB])                                                          S(q)

∞                                                                 ∞
↑                                                                  ↑
C                                                                  Δ

LQG                                                             Regge
transition amplitudes             hbar→0               Hamilton function
W[SUB]C[/SUB](h[SUB]l[/SUB])                                                          S[SUB]Δ[/SUB](l[SUB]i[SUB][U]bdry[/U][/SUB][/SUB])

source paper http://arxiv.org/abs/1108.0832
colloquium talk http://pirsa.org/12040059
concurrent beginner course http://pirsa.org/C12012 e.g. http://pirsa.org/12040019 , 0020, 0021,...

It's nice how things are coming together. There is that excellent introductory course for beginners, running concurrently in online video, that develops this same material at simpler level over several mornings---and there is the oneshot higher level presentation in colloquium, also online video. And there is the August 2011 paper, which in effect the colloquium is explaining, and which gives the gist in compact form you can print out.

 

[atyy]

Yes, at the end, as one of the open problems --- he considers it a question of well-behaveness of radiative corrections. To be concrete, the system he really has in mind is the q-deformed version with a cosmological constant, which makes the sum obviously finite (the representations are bounded from above as well as below). His phrasing of the problem is then that of whether the N-vertex expansion is a useful one, i.e. does the first few terms really provide a good approximation to the full theory.

Isn't the q-deformation supposed to solve a different divergence than the continuum limit, ie. the continuum limit still seems divergent after q-deforming?

By continuum limit, I'm thinking of Eq 26 in http://arxiv.org/abs/1010.1939. The discussion following talks about q-deformation, and the limit of Eq 26 as different things.

 

[genneth]

Isn't the q-deformation supposed to solve a different divergence than the continuum limit, ie. the continuum limit still seems divergent after q-deforming?

By continuum limit, I'm thinking of Eq 26 in http://arxiv.org/abs/1010.1939. The discussion following talks about q-deformation, and the limit of Eq 26 as different things.

It would solve both. The sums that are in Eq 25 of that paper become completely finite --- there are literally only a finite number of terms which contribute.

 

[marcus]

Links to Rovelli's online video course in LQG, which goes along well with the source paper On the Structure of a Background Independent Quantum Theory and with the colloquium talk Transition Amplitudes in QG
that we are considering, will be given here http://pirsa.org/C12012

Lecture 1 http://pirsa.org/12040019
Lecture 2 http://pirsa.org/12040020
Lecture 3 http://pirsa.org/12040021
Lecture 4 http://pirsa.org/12040022

Lecture 5 http://pirsa.org/12040026
Lecture 6 http://pirsa.org/12040027 expected
Lecture 7 http://pirsa.org/12040028 "
Lecture 8 http://pirsa.org/12040029 "

The first 5 lectures are now online. Hopefully there will be a third week as well.
For reference:
On the Structure... http://arxiv.org/abs/1108.0832
Transition Amplitudes...http://pirsa.org/12040059

 

[atyy]

It would solve both. The sums that are in Eq 25 of that paper become completely finite --- there are literally only a finite number of terms which contribute.

Yes, Eq 25 would be finite under q-deformation, but how about Eq 26, where C -> ∞ ?

 

[genneth]

Yes, Eq 25 would be finite under q-deformation, but how about Eq 26, where C -> ∞ ?

One needs to keep in mind that an amplitude is always associated with a boundary state. If you keep adding vertices then eventually the only way to satisfy the tetrahedral inequalities will be to force some faces to be of zero size due to area quantisation. In other words, you can't actually keep refining if the boundary state itself is finite.

The q-deformation just ensures that the boundary state will be.

 

[atyy]

One needs to keep in mind that an amplitude is always associated with a boundary state. If you keep adding vertices then eventually the only way to satisfy the tetrahedral inequalities will be to force some faces to be of zero size due to area quantisation. In other words, you can't actually keep refining if the boundary state itself is finite.

The q-deformation just ensures that the boundary state will be.

Wouldn't that mean that spin foams won't match the (full) state space of canonical LQG?

 

[marcus]

Now I can complete the listing in the previous slide #16. Rovelli's online video course in LQG, which goes along well with the source paper On the Structure of a Background Independent Quantum Theory and with the colloquium talk Transition Amplitudes in QG that we are considering in this thread, is expected to run for 14 lectures, through 20th April. http://pirsa.org/C12012 If you have watched the lectures and can do so, feel welcome to suggest corrections to my tag summaries.

Lecture 1 http://pirsa.org/12040019 what are Q theory and geometry basically about?, the quantum tetrahedron
Lecture 2 http://pirsa.org/12040020 historical and philosophical perspective on QG
Lecture 3 http://pirsa.org/12040021 Hamilton function, physics w/o preferred time coord.
Lecture 4 http://pirsa.org/12040022 quantum physics w/o time: transition amplitudes

Lecture 5 http://pirsa.org/12040026 gravity. formulated in Palatini&Holst actions. overview of how discretized, quantized.
Lecture 6 http://pirsa.org/12040027 simpler worked example of quantizing 3D Euclidean gravity
Lecture 7 http://pirsa.org/12040028 math: specific graph Hilb. space&operators, SU(2) reps, spinnet basis.
Lecture 8 http://pirsa.org/12040029 expected Th 12 April
Lecture 9 http://pirsa.org/12040030 " F 13

Lecture 10 http://pirsa.org/12040033 " M 16
Lecture 11 http://pirsa.org/12040034 " T 17
Lecture 12 http://pirsa.org/12040035 " W 18
Lecture 13 http://pirsa.org/12040036 " Th 19
Lecture 14 http://pirsa.org/12040037 expected F 20 April

The first 7 lectures are now online.
For reference:
On the Structure... http://arxiv.org/abs/1108.0832
Transition Amplitudes...http://pirsa.org/12040059
====================
2012 seems to be a teaching year. Effective pedagogical resources are being developed to help bring young researchers into the field and get them up to speed. New research centers are being established. To fill out and balance the picture I will add a reminder about the Beijing Loop-and-allied QG school to be held 12 - 18 August, 2012 at Beijing Normal University.
Topics:
Loop quantum gravity, Loop quantum cosmology, Spin foams, Regge calculus, Group field theory.
Lecturers:
Abhay Ashtekar (Penn State, USA)
Benjamin Bahr Cambridge Univ, UK)
John Barrett (Univ of Nottingham, UK)
Jonathan Engle (Florida Atlantic Univ, USA)
Thomas Krajewski (Univ of Provence, France)
Jerzy Lewandowski (Univ of Warsaw, Poland)
Etera Livine (Ecole Normal Univ of Lyon)
http://physics.bnu.edu.cn/summerschool/en/index.php

Just an incidental note: The week of 23 April there will be the Field Theory and Gravitation School near Rio de J in Brazil, and Martin Bojowald will be giving two lectures on the topic:
Loop quantum gravity, canonical effective theory, and space-time structure

Loop quantum gravity is a canonical quantization of gravity which implies discrete structures of quantum geometry. In such a setting, it is important to develop tools of effective equations in order to derive physical implications at energies far below the Planck scale. Canonical techniques for effective equations then illustrate several properties of quantum cosmology and of space-time structure on small distances, of potential relevance for confrontations of theory and observations. The methods used combine several aspects of field theory and gravitation.​

http://sixthschool.unila.edu.br/?pagina=resumos&idioma=en

Each of the invited speakers will give two one-hour lectures. Steve Carlip divides his time between two topics:
Spontaneous Dimensional Reduction?
and
Effective Conformal Descriptions of Black Hole Entropy

John Donoghue will devote both hours to Effective Field Theory and General Relativity
That's just a sample, there are many more.

 

[member 11137]

Now I can complete the listing in the previous slide #16. Rovelli's online video course in LQG, which goes along well with the source paper On the Structure of a Background Independent Quantum Theory and with the colloquium talk Transition Amplitudes in QG that we are considering in this thread, is expected to run for 14 lectures, through 20th April. http://pirsa.org/C12012 If you have watched the lectures and can do so, feel welcome to suggest corrections to my tag summaries.

Lecture 1 http://pirsa.org/12040019 what are Q theory and geometry basically about?, the quantum tetrahedron
Lecture 2 http://pirsa.org/12040020 historical and philosophical perspective on QG
Lecture 3 http://pirsa.org/12040021 Hamilton function, physics w/o preferred time coord.
Lecture 4 http://pirsa.org/12040022 quantum physics w/o time: transition amplitudes

Lecture 5 http://pirsa.org/12040026 gravity. formulated in Palatini&Holst actions. overview of how discretized, quantized.
Lecture 6 http://pirsa.org/12040027 simpler worked example of quantizing 3D Euclidean gravity
Lecture 7 http://pirsa.org/12040028 math: specific graph Hilb. space&operators, SU(2) reps, spinnet basis.
Lecture 8 http://pirsa.org/12040029 expected Th 12 April
Lecture 9 http://pirsa.org/12040030 " F 13

Lecture 10 http://pirsa.org/12040033 " M 16
Lecture 11 http://pirsa.org/12040034 " T 17
Lecture 12 http://pirsa.org/12040035 " W 18
Lecture 13 http://pirsa.org/12040036 " Th 19
Lecture 14 http://pirsa.org/12040037 expected F 20 April

The first 7 lectures are now online.
For reference:
On the Structure... http://arxiv.org/abs/1108.0832
Transition Amplitudes...http://pirsa.org/12040059
====================
2012 seems to be a teaching year. Effective pedagogical resources are being developed to help bring young researchers into the field and get them up to speed. New research centers are being established. To fill out and balance the picture I will add a reminder about the Beijing Loop-and-allied QG school to be held 12 - 18 August, 2012 at Beijing Normal University.
Topics:
Loop quantum gravity, Loop quantum cosmology, Spin foams, Regge calculus, Group field theory.
Lecturers:
Abhay Ashtekar (Penn State, USA)
Benjamin Bahr Cambridge Univ, UK)
John Barrett (Univ of Nottingham, UK)
Jonathan Engle (Florida Atlantic Univ, USA)
Thomas Krajewski (Univ of Provence, France)
Jerzy Lewandowski (Univ of Warsaw, Poland)
Etera Livine (Ecole Normal Univ of Lyon)
http://physics.bnu.edu.cn/summerschool/en/index.php

Just an incidental note: The week of 23 April there will be the Field Theory and Gravitation School near Rio de J in Brazil, and Martin Bojowald will be giving two lectures on the topic:
Loop quantum gravity, canonical effective theory, and space-time structure

Loop quantum gravity is a canonical quantization of gravity which implies discrete structures of quantum geometry. In such a setting, it is important to develop tools of effective equations in order to derive physical implications at energies far below the Planck scale. Canonical techniques for effective equations then illustrate several properties of quantum cosmology and of space-time structure on small distances, of potential relevance for confrontations of theory and observations. The methods used combine several aspects of field theory and gravitation.​

http://sixthschool.unila.edu.br/?pagina=resumos&idioma=en

Each of the invited speakers will give two one-hour lectures. Steve Carlip divides his time between two topics:
Spontaneous Dimensional Reduction?
and
Effective Conformal Descriptions of Black Hole Entropy

John Donoghue will devote both hours to Effective Field Theory and General Relativity
That's just a sample, there are many more.

Just two remarks:
1°) Thank you for this possibility to learn at home or everywhere;
2°) Concerning a more technical point which is treated in lecture 5 (after 15'); I try to understand (just starting my way) the construction of LQG and quantization procedures in general. I am a little bit in trouble concerning the question of the triad (or tetrad) formulation. Rovelli claims that it is a strategic tool for the writing of the Dirac's equation. On another approach (arXiv: gr-qc/9806041 - QT of Geometry III, Non Commutat.. of Riemann structures), the triad is described as unappropriate tool... I am lost. Where is the truth?
Thanks

 

[genneth]

Just two remarks:
2°) Concerning a more technical point which is treated in lecture 5 (after 15'); I try to understand (just starting my way) the construction of LQG and quantization procedures in general. I am a little bit in trouble concerning the question of the triad (or tetrad) formulation. Rovelli claims that it is a strategic tool for the writing of the Dirac's equation. On another approach (arXiv: gr-qc/9806041 - QT of Geometry III, Non Commutat.. of Riemann structures), the triad is described as unappropriate tool... I am lost. Where is the truth?
Thanks

I think they (Rovelli and Asheketar) are discussing different aspects. Rovelli's point is only that using the tetrad/triad formalism brings the action into a polynomial form, and which looks similar to local gauge theories, which is good because we kind of know how to do quantisation of those. On the other hand, the quantisation procedure he then pursues is actually quite different from how (say) QCD is done.

Asheketar's paper essentially points out that you can't just go and quantise the tetrad itself, but Rovelli isn't doing that (there's a bit of cunning hidden in the discretisation), so it's okay. Notice that the representation he eventually uses is actually in the connection, rather than the tetrad field.

 

[marcus]

Update on Rovelli's online video course in LQG, which goes along well with the source paper On the Structure of a Background Independent Quantum Theory and with the colloquium talk Transition Amplitudes in QG that we are considering in this thread, and is expected to run for 14 lectures, through 20th April. http://pirsa.org/C12012 If you have watched the lectures and can do so, feel welcome to suggest corrections to my tag summaries.

Lecture 1 http://pirsa.org/12040019 what are Q theory and geometry basically about?, the quantum tetrahedron.
Lecture 2 http://pirsa.org/12040020 historical and philosophical perspective on QG.
Lecture 3 http://pirsa.org/12040021 Hamilton function, classical physics w/o preferred time coord.
Lecture 4 http://pirsa.org/12040022 quantum physics w/o time: transition amplitudes.

Lecture 5 http://pirsa.org/12040026 gravity. Palatini&Holst actions. overview of how discretized, quantized.
Lecture 6 http://pirsa.org/12040027 simple worked example: quantizing 3D Euclidean case.
Lecture 7 http://pirsa.org/12040028 math: specific graph Hilbert space&operators, SU(2) reps, spinnet basis.
Lecture 8 http://pirsa.org/12040029 3D Euclidean example continued: defining transition amplitudes.
Lecture 9 http://pirsa.org/12040030 "the real world" of 4D Lorentzian gravity.

Lecture 10 http://pirsa.org/12040033 (to be gven by Eugenio Bianchi) M 16
Lecture 11 http://pirsa.org/12040034 (Eugenio Bianchi) T 17
Lecture 12 http://pirsa.org/12040035 W 18
Lecture 13 http://pirsa.org/12040036 Th 19
Lecture 14 http://pirsa.org/12040037 F 20 April

The first 9 lectures are now online.
For reference:
On the Structure... http://arxiv.org/abs/1108.0832
Transition Amplitudes...http://pirsa.org/12040059

 

[genneth]

I have to say, I think this lecture series is fantastic. Nevermind whether the 4D Lorentzian theory is actually true, I think this might be the largest "airing" of the work that the loop community has done. There are *lots* of mathematical theorems which are interesting in and of themselves --- the structure of covariant/parameterised systems, fun facts about group theory and representations and functions on them, historical fun (the latest lecture had a line about "then magic, magic and magic" regarding the semiclassical expansion of the 6j symbol).

Personally, I became interested in LQG about 4 years ago (around the time that Rovelli wrote his great, but also greatly flawed, book), and ever since I've been surprised by the general lack of interest in the work. I mean, it's not that hard to understand (compared to, say, string theory) and even as a mathematical curiosity is quite fun. I guess I find the elementary-ness of it all quite appealing, as opposed to problematic.

 

[member 11137]

I think they (Rovelli and Asheketar) are discussing different aspects. Rovelli's point is only that using the tetrad/triad formalism brings the action into a polynomial form, and which looks similar to local gauge theories, which is good because we kind of know how to do quantisation of those. On the other hand, the quantisation procedure he then pursues is actually quite different from how (say) QCD is done.

Asheketar's paper essentially points out that you can't just go and quantise the tetrad itself, but Rovelli isn't doing that (there's a bit of cunning hidden in the discretisation), so it's okay. Notice that the representation he eventually uses is actually in the connection, rather than the tetrad field.

Thanks for taking time and for explaining these complicated item. I believe that I understand what you say. Perhaps should it be the starting point for another discussion but if the tetrad cannot be quantized and if mass is equivalent to energy, because the latter must be itself quantized, then -considering the Dirac's equation- you arrive to the heuristical conclusion that the operator itself contains the informations concerning the quantization of the mass-energy. Does it mean that the quantized mass-energy must be an eigenvalue of that covariant derivative operator? If this conclusion is correct, then the theory should be developped around the notion of quantization of derivative operators... Sorry if it is not the good place to discuss about this.

 

[genneth]

Thanks for taking time and for explaining these complicated item. I believe that I understand what you say. Perhaps should it be the starting point for another discussion but if the tetrad cannot be quantized and if mass is equivalent to energy, because the latter must be itself quantized, then -considering the Dirac's equation- you arrive to the heuristical conclusion that the operator itself contains the informations concerning the quantization of the mass-energy. Does it mean that the quantized mass-energy must be an eigenvalue of that covariant derivative operator? If this conclusion is correct, then the theory should be developped around the notion of quantization of derivative operators... Sorry if it is not the good place to discuss about this.

I think you are confused about how the discretisation really works, especially in the presence of Yang-Mills (and attendent fermion) fields. I would suggest taking a look at the lattice QCD literature, and understand how (classical) loop variables work. Intuitively, we write a basis for the (in this case, matter) fields as open strings of holonomy in the gauge field, terminated by two fermions, such that the whole string is gauge invariant.

These loops can be discretised very nicely on a spin-foam by taking the integrated quantities and laying them out along the simplicial structure appropriately.

Another avenue to approach the same topic is discrete differential geometry, which is pure mathematics but has considerable moral overlap with the topic at hand.

 

[TrickyDicky]

Nevermind whether the 4D Lorentzian theory is actually true

Could you give some written reference on this? I'm new to LQG.

 

[genneth]

Could you give some written reference on this? I'm new to LQG.

Please make a new thread somewhere else about this --- I'd like to keep this thread on topic.

 

[TrickyDicky]

Please make a new thread somewhere else about this --- I'd like to keep this thread on topic.

I was asking about one of the lectures (9) from your comment on it, (I was just asking references in the form of arxiv papers but I see Marcus has already given some) is it not this the topic of this thread? If not please clarify what is the topic.
Actually after a second reading your comment is a bit ambiguous, are you suggesting the "real world" 4D lorentzian theory (GR) is not actually true? Oops, maybe this is what you considered off topic right?

 

[genneth]

I was asking about one of the lectures (9) from your comment on it, (I was just asking references in the form of arxiv papers but I see Marcus has already given some) is it not this the topic of this thread? If not please clarify what is the topic.
Actually after a second reading your comment is a bit ambiguous, are you suggesting the "real world" 4D lorentzian theory (GR) is not actually true? Oops, maybe this is what you considered off topic right?

It seems I misunderstood the request. Good thing marcus is reliable :-)

As far as "true" goes, no one knows. We merely have a theory that might be (strong, but not direct evidence) self-consistent, and consistent with classical GR. That is all.

Also, as far as references go, I would say that these lectures should be regarded as the primary and canonical reference right now. These are the clearest, pedagogical and most concise (that is, unburdened by the tortuous route of history) presentation of the theory that exist.

 

[TrickyDicky]

Also, as far as references go, I would say that these lectures should be regarded as the primary and canonical reference right now. These are the clearest, pedagogical and most concise (that is, unburdened by the tortuous route of history) presentation of the theory that exist.

Ok, that's great, I'll watch them.

 

[marcus]

Ok, that's great, I'll watch them.

FWIW I'll tell you my experience. I started with Lecture 3 and in retrospect I would do that again and invite you to do likewise, if it works for you. Lectures 3 and 4 present the "timeless path integral" formalism on which the rest is built.
Alternatively, if you have read "On the Structure..". http://arxiv.org/abs/1108.0832, since that is what Lectures 3 and 4 cover, you could start with Lecture 5, which is where the development of GR and QG starts.

The second thing is I've found it helpful to download the "slides" PDFs and have all 7 icons on my desktop. Actually they are a series of blackboard "stills", not slides. So now I can click immediately on the stills PDF of any of the Lectures 3-9 whenever I want to be reminded of what was covered in that lecture. It takes a couple of minutes to download each PDF, but then it's done.

Lecture 3 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040021
Lecture 4 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040022

Lecture 5 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040026
Lecture 6 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040027
Lecture 7 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040028
Lecture 8 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040029
Lecture 9 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040030

I think scrolling down the fifty to hundred still-frame shots of the blackboard, from a given lecture, could have been baffling or meaningless to me before I actually watched the lecture. The stills hardly speak for themselves. But once having watched and listened, I find that looking back at the blackboard stills is an easy way to recall the main points.

Lectures 3 (resp. 4) review a neat way of treating classical (resp. quantum) mechanics without a preferred time. It is for a general system, not yet specialized to gravity. Lecture 3, classical mechanics without time, is about the Hamilton function (of initial and final configurations of the system). Lecture 4, quantum mechanics without time, is about transition amplitudes (from initial to final states of the system).

In case anyone is new to it, in rough terms the classical Hamilton function, given initial and final, tells you a quantity which is the least action given that choice of initial and final. In other words it gives you the action associated with whatever the classical solution is, if one exists given that choice. Happily it carries over to the "generally covariant" case of classical GR---with very little trouble it can be formulated without preferred time. This gives a clean way of describing both classical and quantum evolution relationally, without commitment to anybody's clock.

In a sense, the Hamilton function (like the transition amplitude) is a function of system boundary variables, like input and output, rather than what happens in between. It is the classical object most closely analogous to the path integral transition amplitude---when quantum mechanics is done without preferred time, in a generally covariant way.

These two things, Hamilton function and transition amplitude, are central to what's being presented, so for anyone not familiar with their treatment without preferred time (On the Structure... http://arxiv.org/abs/1108.0832) Lectures 3 is a good place to start. What then follows in Lecture 5 is to define Palatini and Holst actions for gravity (and starting at minute 40, work out the simplified 3d gravity case.)

It could be that another person would find it better to start with the first two lectures---which give motivation, historical perspective, and a possible intuitive answer to "what is quantum gravity about?".
Reduced to the most basic elementary level, the answer could be paraphrased as follows: Take what you should have learned about the tetrahedron in high school (volume, face areas, normals...), subject that to just one quantum ansatz, the Heisenberg uncertainty principle, and see what a circus erupts from this simple opening move. I listened to Lectures 1 and 2 mostly after watching the formal development in the other talks.

 

[TrickyDicky]

Thanks for the advice and the links, Marcus, really interesting stuff.

 

[marcus]

I have to say, I think this lecture series is fantastic. Nevermind whether the 4D Lorentzian theory is actually true, I think this might be the largest "airing" of the work that the loop community has done. There are *lots* of mathematical theorems which are interesting in and of themselves --- the structure of covariant/parameterised systems, fun facts about group theory and representations and functions on them, historical fun (the latest lecture had a line about "then magic, magic and magic" regarding the semiclassical expansion of the 6j symbol)...

I completely agree! I find I gain understanding of some math tools better after seeing them used ingeniously in geometry (Wigner matrices, j-symbols, representations, quantum groups). This context adds motivation and interest. You referred to Lecture 8 here---the excited exclamation about the 6j symbol was around minute 44.

I think Lectures 8 and 9 are the finest so far---fast clear illuminating delivery. I feel as if I should make a brief outline, of at least those two, maybe Lecture 5 as well, to deepen my understanding, maybe our shared understanding as well.

 

[marcus]

Since we're on a new page I'll recopy links to Rovelli's online video course in LQG, which goes along with the colloquium talk Transition Amplitudes in QG that we are considering in this thread. It's expected to run three weeks: 14 lectures through 20th April. http://pirsa.org/C12012 If you have watched the lectures, feel welcome to emend my summary/outline or contribute your own.

Lecture 1 http://pirsa.org/12040019 what are Q theory and geometry basically about?, the quantum tetrahedron.
Lecture 2 http://pirsa.org/12040020 historical and philosophical perspective on QG.
Lecture 3 http://pirsa.org/12040021 Hamilton function, classical physics w/o preferred time coord.
Lecture 4 http://pirsa.org/12040022 quantum physics w/o time: transition amplitudes.

Lecture 5 http://pirsa.org/12040026 putting GR in the picture. deriving and motivating Palatini&Holst actions. overview of how discretized, quantized in 4d. At minute 40, begin working out toy model (3D Euclidean case) which will be copied in Lecture 9 to get the "real world" case.
Lecture 6 http://pirsa.org/12040027 continue simple worked example: quantizing 3D Euclidean case. How to get from Palatini/Holst classical continuous action to the spin foam.
Lecture 7 http://pirsa.org/12040028 math tools: specific graph Hilbert space&operators, SU(2) reps, spinnet basis.
Lecture 8 http://pirsa.org/12040029 concluding the 3D Euclidean example: defining transition amplitudes. Minute 18 = partition function (which give transition amplitudes when boundary is introduced). Minute 30 - 34= Wigner 6j appear. Minute 44=Ponzano&Regge recover GR! Minute 48=how bubble divergence can arise. How Turaev-Viro cured that using the quantum group of SU(2). How cosmological constant appears in the theory.
Lecture 9 http://pirsa.org/12040030 Beginning "the real world" 4D Lorentzian case.

Lecture 10 http://pirsa.org/12040033 (Eugenio Bianchi) M 16
Lecture 11 http://pirsa.org/12040034 (Eugenio Bianchi) T 17
Lecture 12 http://pirsa.org/12040035 W 18
Lecture 13 http://pirsa.org/12040036 Th 19
Lecture 14 http://pirsa.org/12040037 F 20

The first 9 lectures are now online.
For reference:
On the Structure... http://arxiv.org/abs/1108.0832
Colloquium Transition Amplitudes...http://pirsa.org/12040059
Background Zakopane Lectures... http://arxiv.org/abs/1102.3660

If anyone wants to download blackboard still shots PDF for some of the lectures, to have for reference and review, here are the PDF links.

Lecture 5 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040026
Lecture 6 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040027
Lecture 7 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040028
Lecture 8 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040029
Lecture 9 http://pirsa.org/pdf/loadpdf.php?pirsa_number=12040030

I put them on my desktop to have handy. Once I've listened to a lecture, looking back at the stills is an easy way to recall the main points.