# The Carlo Rovelli book on loop quantum gravity

1. Mar 21, 2006

### Sauron

I had studied LQG using the thieman articles (mostly the brief of around 80 pages) and some other brief reviews (the one on living reviews on gnernal relativity for example) and also i had readed some articles announced in the threads wich maintains Marcus.

But i wanted a most serious lloking so i am now studiying the draft wich is in carllos website.

And i must say that althought it tries to be pedagogical the way i am not sure if it does acomplish the task.

To begin with if i wouldn´t have any previous knowledge in the subjecto i would have understood anything. Now i am begining the chapter four and the way it introduces the theme, making it depend on that hamilton jacobi equations (althought he call´s it hamiltonian) is very bizarre.

May be it is my problem? Do you like that book?

2. Mar 21, 2006

### f-h

It's not you, I'm having the precise problem you are describing, I did start with Rovellis book and got pretty well stuck. Smolins introductory course is great though.

The book appears superficially to be pedagogical, but it actually is incredible dense, surprisingly comprehensive, axiomatic, to a degree idiosyncratic, and not a good place to start learning about LQG IMO, at least if you're unaided.

Most of the reformulations of established physics just make little sense if you don't know the goal he's shooting for, some of these goals are still floating and/or unpublished.

I think the book is best as a companion rather then a guide.

3. Mar 21, 2006

### marcus

fairly put.
agreed.

4. Mar 21, 2006

### Sauron

Glad you agree. I was begining to be worried.

I guess that the main goal of the first chapters is trying to make a brain wash up (hope it is said so) about the "no time hipothesis".

I am currently triying to develope an escenary where in ordinary quantum mechanics you consider the wave function as representing not just the probability of finding a particle in a certain situation of space but also in a certain situation of time and I tried to compare their correlative time and the thermal time hipothesis with my own idas.

That was a hint for motivation. But now i am somewhat frustrated with all that diferent, althought similar, attacks to the actual core of the theory.

May be these thread could be used to ask question wich may be some of you could consider trivial (assuming i have no problems agian with my internet connection).

5. Apr 12, 2006

### Sauron

But ina fewof theses articles i hhave found a repeated feture.They seem very worried about finding an expresion for the symplecthic structure.

And once that they findi don´t see they use it at all.

In the first chapters of the book Roveely introduces from scracth symplettic geometry.I had some previous knowledge of the subjecto froma book by sysoph "tensor analysys on manifolds" and also from a book of V.I Arnold in mathemathical methos on mechanics.

But i dónt end to see the relevance of the symplectic formulation of clasical mechanics. Not to say in quantum gravity. I think i have got a resonable understanding of some aspectos of LQG and i dón´t see wich the relevance of these symplectic mechanics is. ¿any advice?

And a question off-topic,i have just discovered, reading a post of self-adjoint, that these forums support latex ¿Wich tag must i use for typing latex equations?

6. Apr 12, 2006

### marcus

the word "tex" in brackets, and "/tex" in brackets
if you look at someone else's and say "quote" as if you intend to reply, then it will show how all the equations are spelled, with the tags

so I put a space to keep it from working and then take the space away

[t ex]\hbar G_N/c^3[/t ex]

$$\hbar G_N/c^3$$

[t ex]\frac{\hbar G_N}{c^3}[/t ex]

$$\frac{\hbar G_N}{c^3}$$

There is a LaTex thread on PF

Last edited: Apr 12, 2006
7. Apr 13, 2006

Staff Emeritus
8. Apr 13, 2006

### Sauron

Ok, thanks by the help in latex. In an spanish forum i use thhey have anicon in the reply form wich adds the tag so it was more obvious their latex support.

About the other question i think i have found the key question myself reading the short explanation in wikipedia aobuth symplectic geometry:

http://en.wikipedia.org/wiki/Hamiltonian_vector_field

I guess the key point I was missing is the use of the symplectic two form as a help in the calculation of the poisson brackets.

9. Apr 13, 2006

Staff Emeritus
Yes, in the Hamiltonian formulation, the phase space, or rather the subspace in it traced out by the dynamics, is a symplectic manifold, which is the background of that symplectic form you discovered.

10. Apr 13, 2006

### josh1

In classical mechanics in n-dimensional spacetime, states are represented as points in a 2n-dimensional phase space manifold M. The advantage of the symplectic formulation is that it frees one of having to choose a specific set of linear canonical coordinates on M.

In quantum mechanics, states are not points in a finite-dimensional phase space M, but vectors in an infinite-dimensional Hilbert space. The advantage of the symplectic formulation here is that it straightforwardly generalizes to this infinite-dimensional case.

11. Apr 13, 2006

### Sauron

Hum, lets see if understand correctly and i relate it wiht something i have readed when the talk about "prequantization".

Let´s say that inlagrangian mechanics i have a configuration manifold. The tangent space (or tangle bundle) of these is the phase space. So I have a "natural" way to separate coordinates and momenta. In fact it is the symplectic form wich makes a natural isomorphism betwen the tangent and cotangent bunle.

But if i specify anarbitrary manifold and i can suply it with a symplectic form i can see it as a phase space. And even more i can choose an isotropic maximal dimension manifold (that in wich the symplectic form vanish). (as I can see in http://en.wikipedia.org/wiki/Symplectic_manifold)

P.S. Belive it or not symplectic geometry is not studied in my university nor in the physic graduate nor in the math graduate. And to study thing by myself has it´s drawbacks.

12. Apr 14, 2006

### josh1

Yeah, I'd say that's pretty much right on the money :rofl:

13. Apr 20, 2006

### Sauron

Well, he would deserve a hughe money for his work them, he is very dedicated at the labour

Sorry to once agian interfere your discusions in the very last published articles to ask for reading guide.

Afther reareading of the reviews in LQG (canonical theory) I went to apliactions. I readed completely a review of 2003 of Bojowald of loop quantum cosmology, and partly the review in living reviews. Also i readed the Astekhar-Bojowald and the Bojowald alone reviews in black holes singularities (i have a few questions on these wich i´ll make somewhere else)

I think i have a reasonable understanding of these topics. Now i am confused in what to study next.

May be spin-foam models. But what i have seem a very good starting point could be these article http://arxiv.org/PS_cache/gr-qc/pdf/0301/0301113.pdf [Broken]

Also i am interested in the graviton question. I have seen evolution in the way LQG studies gravitons. In the review article of thieman he mentions the line of investigation related to these article http://arxiv.org/PS_cache/gr-qc/pdf/0204/0204067.pdf [Broken]

Even thought nowadays it seems that the line of attack has changed and it is based in the lines of these article arXiv:gr-qc/0508124

and his continuation http://arxiv.org/PS_cache/gr-qc/pdf/0604/0604044.pdf [Broken]

These last two articles seems to depend strongly in the spin foam models.So i would need to study it. And that brings me back to the article on spin-foams would it be a good starting point? Or should i try to read the corresponding chapters in the Rovellis book?

As far as i have understood there is a thrid line of investigation in LQG, that of causal triangulations, wich semmengly overlap with the spin-foam one , am i right? -wich would you recomend to study first? (and wich paper to use to begin with dynamical triangulations if that would be the choice)

Last edited by a moderator: May 2, 2017
14. Apr 20, 2006

### marcus

I am honored by your praise, even if slightly ironical
But in fact it is YOUR diligence that merits praise. You have really been working hard studying Quantum Gravity.

You mention the most recent Rovelli graviton paper
http://arxiv.org/gr-qc/0604044 [Broken]
One study method would be to determine what it takes to understand that paper and learn only that.
I am not sure what to suggest.

1. One thing would be to write Alejandro Perez email and ask him directly "what shall I read in order to prepare to understand Rovelli et al graviton paper?"
He is a close associate of rovelli and he is a spinfoam expert.

2. Another thing might be to start a thread here at PF "Loop graviton study suggestions?" or something like that. You might get some advice from F-H who posts here and is an unnamed grad student member of the rovelli team at Marseille. Or someone else might think of some advice to give.

3. Another option is to watch the Smolin Lectures #19, 20, 21 which are online at the Perimeter streaming media site. These 3 lectures are given by Daniele Oriti. He is an excellent lecturer, cool-headed, crisp and organized. Spinfoam is the subject of #19, 20. and then the subject of #21 is Group Field Theory (GFT).

Oriti is at Cambridge and he is a leading SpinFoam expert. I would not write email to him because he is busy preparing his book for publication (supposedly this year). If you watch the video lectures you will get a selfcontained overview of SpinFoam and this will suggest some reading.

BTW IIRC Oriti's PhD thesis (at arxiv) is a survey of SpinFoam including the underlying philosophy. It might be an alternative introduction.

I recommend to begin BOTH AT ONCE. Begin to learn Loll CDT lightly at the same time as begin SpinFoam seriously (Loll would be angry if she heard someone say this).
the reason I say this is that for me CDT is very illuminating and beautiful-----also I love it that one can do MONTE CARLO COMPUTER SIMULATIONS OF THE UNIVERSE----it is almost like a kind of laboratory experiment, one can allow universes to create themselves ex nihilo, and then one can wander through them and explore them and discover if they have the right dimension etc.

for me, this was the way that Quantum Gravity was always meant to be.
So I would say to begin lightly reading THE UNIVERSE FROM SCRATCH which is Loll's 2005 intro paper.
http://arxiv.org/abs/hep-th/0509010

But at the same time, realize that it is SpinFoam and GFT that is the doorway to ALL THE NEW 2006 RESULTS! this is a serious problem. Loll CDT is beautiful but I do not know any important new result since Summer of 2005.
Meanwhile in SpinFoam there is Freidel work including matter and feynman diagrams----and there is the Rovelli graviton papers that you mentioned.

Please excuse my giving you a very personal perspective on this. Again, why not write one of the experts a short email inquiry, e.g. to Alejandro Perez? Do you lack his email address?

Last edited by a moderator: May 2, 2017
15. Apr 20, 2006

### francesca

Very Italian!

Rovelli book seems to me very Italian, in the sense that in Italy we introduce symplectic manifold at the second year of ungraduate courses... but I have no text to advise, I've studied only texts in Italian, except Arnold!

16. Apr 20, 2006

### Sauron

Alejandro Perez is Arivero isn´ it?

I have no practice to write mails to people actually workin in an university . Maybe they could angry.

I must say that i am surprised with the relevance of spin foam models afther Baez saying once and again that he ahd failled to get what he expected from them. In fact i beguined to read a review from Baez,and i saw it was mostly TFT (as far as i reached to understand).

It had let me to watch them just like maths. That, of course, is not bad, but i was not looking more math in these times (except the one i must take exams to end my math degree, mostly informatic oriented).

Anyway, i have opted,because you say he is an expert, to study the artiicle of 2003 of Alejandro, wich looks very pedgogical, i hope things have not changed too mcuh since them. And anyway, i also hope i could upgrade to most recents versions from that.

About the Renata Loll et all that you linkedi´ll give it a sight these night.

P.S. Francesca, that looks surprising for me. how is that you know manifolds (and so set topology), in a second course of physics.

In my university (in maths) you study set topology and classical diferential geometry in the second year, manifold diferential geometry in third. In the old plain (when i studied that things) riemanian geometry in fourth course (now it is not studied). You get some about bundle theory in 5th course in a seminary asignature. In physics we simply didn´t study any modern math (except for a fast intro to diff geometry given by E. Alvarez in 5th to explain general relativity and cosmology).

I guess your are more ready for modern life that in my university.

Last edited: Apr 20, 2006
17. Apr 20, 2006

### marcus

no, arivero is Alejandro Rivero of university zaragoza Spain

Perez is at the CPT at Marseille (center physics theoretical).

perez has never come here to PF as far as I know (perhaps he does not appreciate the finer things in life the way arivero does)

18. Apr 20, 2006

### marcus

If you wish, please mention of few of the best texts in Italian, some people at PF read Italian and might be interested.

19. Apr 20, 2006

### francesca

What do you mean with modern math? Well, for exemple about categories theory my professors told me nothing more than it exist!
Referring to old plan (when i attended courses, then few years ago all things have changed) the curriculum in physics provided starting from the first year two courses in analysis in which we studied also set topology, manifolds and so on. We used that books:
G. De Marco Analisi I, Analisi II ed. Decibel-Zanichelli
(I don't have a lot of other books to advice Marcus! but viceversa i like your suggestion)
At the second year we had "meccanica razionale" in which we studied analytic mechanics, lagrangian theory and hamiltonian theory (with simpletic formalism): note that this is the same course Rovelli had taught first in his career!
To complete the list, al the third year we have a course in methods of modern mathematical physics. Note that these were base courses, not only for theorician! But i've said that now is not the same...

ps: Perez isn't old! i suppose he would be kind if you wrote him Sauron!

20. Apr 20, 2006

### ahrkron

Staff Emeritus
Alejandro Perez is a very approachable guy. I'd imagine he will be happy to see people interested in this kind of work. Carlo Rovelli is also very easy to talk to, but he keeps himself quite busy.

21. Apr 20, 2006

### ahrkron

Staff Emeritus
22. Apr 20, 2006

### Kea

Ah! Notice that later on in the same thread there is also a quote of Rovelli's from a pm - poor taste to post such things on a forum, but I've since posted the paragraph that starts

In discussing science, we all make all sorts of mistakes...

on my door.

Kea

23. Apr 20, 2006

### Sauron

Well, basically everything on the style of "let´s take a paracompact subset wich is also hausdorf, then..." that is, things exposed usgin point set topolgy and in general rigurous definitions.

In physics we studied (now its a bit different, and worst) analisis of one variable, vector cauculus and linear algebra in first course. Diferential equations, more linear algebra, some of tensor algebra and tensor analisis, and complex variables in second. Mathematical methods (special funtions, some integral transforms and in general everything in the style of the arfken or matwes walker book in third. Statistic and,if you where in theoretical physics gropup theory (as continuous groups, the teacher didn´t have any idea of what a topolgicla space, nor to say a manifold or diferential forms were, well, at least not before i teached him in the work necessary to can passs the asignature )

I had to get all the modern math in the math licenciature, basically geometry, topology and functional analisys (i only got the asignatures necessary for physic, i am getting the others now).

Feel happy about it. My fvourite branch of maths is topology. So I got the book wich covered more topics in algebraic topolgy to complemente the asignature in fourth of maths. It is writen by Spanier. And it begins introducing the notions of categories and functors betwen them and using it ocasionally. That´s all my knowledge about them.

And it was engought. It is not that i find then particularly difficoult.Simply they looked me unnecesary excess of formalism. When i readed Baez saying they were meant to be the future of LQG I thought theory had died even before reaching it´s infancy, in fact i left the subject behind for a time partly because it. I am glad to see it has not been the case. The work in black holes singularities has renowed my interest in the subjecto (and also seeing that categories seems to have voltilized from it :tongue2: ).

Of course these is a prejudice of my. But in topology I prefer the line of thinking and exposings of the books of Jonh Milnor, and categories don´t appear there xD. I see them usefull for organing ideas but i can´t realise how any basic understunding of something (nor to say quantum gravity) can merge from it (i am very happy to not have any reputation to keep and feel free to say these things withouth a deep knowledge of the matter )

About mechanics i studied in second classical mechanics wich included lagrangian mechancis and aplications. Hamiltonian mechanics. And the las theme was Hamilton Jacobi and action angle variables. Never agian used them. In theoretichan mechanics,fourth course, we saw constrained systems and the Dirac formalism. I sutied a bit of symplectic mechanics myself but never had ended to see the point in it (now thanks to these forum people i see the sense of all that annoying things i had readed just for,er, snobism? . Ok, ok, supossedly i had in the far horizont the idea that it could serve me to understand the demostration of the kolmogrov´s theorem about the stability of the solar system, but i never went so deep.

So that´s why the first chapters of Rovellis books were hard for me. I just saw the exposure of the same things in all the available languajes of mechanics (two of wich were unfamilar for me) withouth seeing a good reason for it.

A propossito Francesca io parlo Italiano e anche posso legerlo senza tropi problemi. Vero e che fago molti errori ma comme puoi ridere anche li fago in anglese, cosi se tu hai qualquna referenza interesanti in italiano per me non chie problema.

As i said a am studing now the 2003 review of Alejandro Perez in spin foams. Good to see that it could be possible to ask him my doubts. Althought if i expose then here maybe someone else has similar doubts and all of as gain something (that´s the reason for these forums, isn´t it?)

P.S. Murphy law strikes again. A lot of papers withouth any mention on categories and when i arrive at page11 of the Alejandro article I read that spin networks define a category and that spin foam theories are morphisms betwen them. Better i should have been quiet.

Last edited: Apr 20, 2006
24. Apr 21, 2006

### francesca

perez foams

Do you have seen also this?
http://arxiv.org/abs/gr-qc/0409061
Introduction to Loop Quantum Gravity and Spin Foams
Authors: Alejandro Perez
Comments: Lectures presented at the II International Conference of Fundamental Interactions, Pedra Azul, Brazil, June 2004. Typos corrected
"These notes are a didactic overview of the non perturbative and background independent approach to a quantum theory of gravity known as loop quantum gravity..."

Surely is more recent, it was posted in 2005, but maybe it's a more general and pedagogical exposition than the paper you're reading...

25. Apr 21, 2006

### marcus

good idea of francesca, to check this out for comparison, since more recent.
posted actually September 2004, but revised as recently as February 2005.

also several people have had praise for Oriti's thesis (not more recent, but a different expository style)
http://arxiv.org/abs/gr-qc/0311066
Spin Foam Models of Quantum Spacetime
Daniele Oriti
337 pages, 31 figures

it would be costly in time and effort to print out the whole, but one can look at selected chapters and compare them with Perez explanations. It is always possible to print out portions, instead of the whole 300 pages.

Last edited: Apr 21, 2006