Researching LQG: What Disciplines Should I Study?

[jvdornas]

Hi,

here in Brazil doesn´t seem to have a researcher specialized in LQG. I think I will have to do my doctorate research in another field and just afterwards study LQG on my own. Could anybody help me to make a list of the disciplines I should study to comprehend and do research in LQG ? Should I study QFT, QFT in curved spacetime, GR, Analysis, Topology (what topology ? algebraic, differential, or both ?), Differential Geometry ? Is that all or there are others ?

I appreciate the help,

jvdornas

 

[PhysiSmo]

Hey there! I believe that http://arxiv.org/abs/hep-th/0408048v3" could provide great help for what you' re looking for. Especially the (pretty long) references list for further reading.

 

[marcus]

Should I study QFT,... GR, Analysis, ..., Differential Geometry ?

Yes.
I took topology off your list. It is good to study but for most current QG you don't need a deep background in it. What you do need you will be able to pick up.

so topology is not so essential as GR, Analysis, Diff.Geom (and Lie Groups)

For a light introduction to core LQG and LQC there is a recent (2007) paper by Ashtekar. look on arxiv.

for a massive, technically formidable treatment of core LQG (and certain recent extensions) there is the forthcoming September 2007 book by Thiemann. It is expensive---you might request that your university library order it so you can use the library copy and don't have to pay for it. It is 650 pages and mathematically self-contained---it covers the various maths you need in a giant appendix.
I know this book only from an earlier draft version and from the Cambridge University Press web-page about it, which has a table of contents.

there is Rovelli's (2004) book which is more conceptual: it has half as many pages and balances technical development with intellectual clear-sightedness. Much has happened since 2003 when the book was written and you must supplement the book with recent papers by Rovelli and others to get an up-to-date picture.

For some reason the image of a jeep and a bulldozer come to mind. each is good at some things
===============

modern QG is a mosaic of different approaches. core LQG and LQC (the application to cosmology) is one important sector.
Another is LQG/SF the approach to LQG using SPINFOAM formalism.
You can get recent papers by searching arxiv for recent work by Rovelli (2005 and later) and by his collaborators.

Another active sector of QG research is GROUP FIELD THEORY (GFT). You can find recent papers by searching arxiv for recent work by Daniele Oriti, and his collaborators. there is also earlier work by Freidel, Krasnov and others but Oriti is a good keyword "search term" to find the literature.

GFT is being presented as a broad comprehensive QG FRAMEWORK, within which one can find LQG/SF, and Dynamical Triangulations (another approach), Regge gravity, and even some Condensed Matter models of gravity that have been appearing.

Another important sector of QG, one that is rapidly growing, is NUMERICAL modeling with supercomputers. Some names to use as search terms, if you want to find the literature on this, are Dan Christensen, David Rideout.

==================
The closest QG to observational testing is associated with Martin Bojowald.
He does Loop Quantum Cosmology (LQC) and closely related effective/perturbative LQG. There are a dozen or so other people but you can find their names by searching for Bojowald papers because sometimes they co-author with him.

This is the most direct line of QG research to get into, using the least-abstract most basic concrete mathematics, the most reliant on physical intuition and familiarity with cosmology. It is the least theoretical QG and the closest to making predictions about galaxy survey statistics (large scale structure) and the Cosmic Microwave Background.
Bojowald has a new paper that verges on making predictions about supernova observations also. This is a new idea and needs more work---it is a possible explanation of DARK ENERGY as a QG effect that would lead to an observably different acceleration history.

My advice to you would actually to try a DIFFERENT path from reading theoretical books and heavy abstract math. I would suggest you just go to arxiv and try to read Bojowald's papers and see what math and physics you actually need.
In a way he is like the airplane pilots that flew the old planes "by the seat of the pants" without elaborate instruments. that is he is constructing a quantum cosmology by physical "feel" starting from very simplified models in 2001 and gradually removing the simplifying assumptions and extending the results 2001-2007.
Even now it is very physical and not too mathematically complicated. And it is clearly beginning to lead to PREDICTIONS which can be tested by observation.

Since you are in Brazil, you could write to a Colombian postdoc named Aureliano Skirzewski----who went from Bogota to Trieste to Berlin and has collaborated with Bojowald and I think is now back in Bogota (but now as an active expert in LQC).
He might have some suggestions for you of what to study
His experience and perspective might be helpful to you, if he is willing to reply to your email.
to find his address just go to arxiv.org search and put in the name Skirzewski---there must be only one :-)

 

[ccdantas]

Oi João!

Here is a list slightly updated from myold (now shutdown) blog

(a backup of this list can be found here: http://www.geocities.com/christinedantas/basic-curriculum-for-quantum-gravity.html )---------------------------------------------------
1) Pre-requisites:

- General Relativity (GR)

In particular: the Hamiltonian formulation of GR:
[1.1] Wald R M, 1984, General Relativity (Chicago: Chicago University Press)

- Quantum Mechanics and Quantum Field Theory (QFT)

[1.2] Zee A 2003 Quantum Field Theory in a Nutshell, Princeton University Press

[Update Jun/07: Quantum Field Theory, by Mark Srednicki, Cambridge U Press]

In particular: QFT in flat and curved space-time:
[1.3] Wald R M, 1994, Quantum field theory in curved space-time and black hole thermodynamics (Chicago: Chicago University Press)

- Gauge Field Theory

[1.4] Baez J and Muniain J P, 1994, Gauge fields, knots and gravity, Singapore: World Scientific -- wait for the upcoming second edition!

[1.5] George Svetlichny, Preparation for Gauge Theory [math-ph/9902027]

- Systems with constraints:

[1.6] Sanjeev S. Seahra, The Classical and Quantum Mechanics of Systems with Constraints

[1.7] Andreas W. Wipf, Hamilton’s Formalism for Systems with Constraints [hep-th/9312078]

[1.8] Paul A. M. Dirac. Lectures on Quantum Mechanics. Dover, Mineola, New York,
1964.

- Mathematical Methods:

[1.9] Frankel T 2003 The Geometry of Physics, Cambridge University Press

[1.10] Bishop R L and Goldberg 1968 Tensor Analysis on Manifolds, Dover

[1.11] Byron F W and Fuller R W 1970 Mathematics of Classical and Quantum Physics, Dover

[1.12] Henle M 1979 A Combinatorial Introduction to Topology, Dover

[1.13] Tung W 1985 Group Theory in Physics, World Scientific

[1.14] Nakahara M 1990 Geometry, Topology and Physics, Institute of Physics Publishing Bristol and Philadelphia2) Standard Books (I find them quite advanced, though):

[2.1] Rovelli C 2004 Quantum gravity (Cambridge, UK: Cambridge University Press)

[2.2] Thiemann T 2001 Introduction to modern canonical quantum general relativity [gr-qc/0110034]

3) Primers:

[3.1] Pullin J, Knot theory and quantum gravity in loop Space: A Primer [hep-th/9301028]

[3.2] Rovelli C and Upadhya P, Loop quantum gravity and quanta of space: A primer [gr-qc/9806079]

[3.3] Major S A, A spin network primer [gr-qc/9905020]

[3.4] Alejandro Corichi, Loop Quantum Geometry: A primer [gr-qc/0507038]

4) Introductory texts and reviews:

[4.1] Ashtekar A, Gravity and the quantum [gr-qc/0410054]

[4.2] Smolin L, An invitation to loop quantum gravity [hep- th/0408048]

[4.3] Ashtekar A and Lewandowski J, Background independent quantum gravity: A status report [gr-qc/0404018]

[4.4] Perez A, Introduction to loop quantum gravity and spin foams [gr-qc/0409061]

[4.5] Thiemann T, Lectures on loop quantum gravity [gr-qc/0210094]

[4.6] Nicolai H, Peeters K and Zamaklar M, Loop quantum gravity: An outside view [hep-th/0501114] (warning: outside view)

[4.7] Rovelli C, The century of the incomplete revolution: Searching for general relativistic quantum field theory [hep-th/9910131]

[4.8] Rovelli C 1998 Loop quantum gravity Living Rev. Rel. 1 1 [gr-qc/9710008]

[4.9] Pullin J Canonical quantization of general relativity: The last 18 years in a nutshell [gr-qc/0209008]

[4.10] Rovelli C, Strings, loops and others: A critical survey of the present approaches to quantum gravity [gr-qc/9803024]

[4.11] Rovelli C, Notes for a brief history of quantum gravity [gr-qc/0006061]

[4.12] Rovelli C, A dialog on quantum gravity [hep-th/0310077]

[4.13] Smolin S, How far are we from the quantum theory of gravity? [hep-th/0303185]

[4.14] Muxin Han, Weiming Huang, and Yongge Ma, Fundamental Structure of Loop Quantum Gravity [gr-qc/0509064]

[4.15] Lee Smolin, The case for background independence [hep-th/0507235]

[4.16] Alejandro Perez, The spin-foam-representation of LQG [gr-qc/0601095]

[4.17] Hermann Nicolai and Kasper Peeters, Loop and Spin Foam Quantum Gravity: A Brief Guide for Beginners [hep-th/0601129] (warning: outside view)5) On-line courses:

- Baez J Quantum Gravity Seminar

- Smolin L, Introduction to Quantum Gravity

-----------------------------------------------
Ashtekar wrote a review paper and a faq recently:

http://arxiv.org/abs/0705.2222

He also wrote an interesting introductory paper:

http://arxiv.org/abs/gr-qc/0702030

---------------------------------------------------------------------------------

Perhaps others here at PF will offer you some other insights... It's a nice place to post your questions.

And let us keep in touch. There is also another student here in Brazil with whom I am in contact. He is looking for a postdoc in LQG in a couple of years. Christine

 

[marcus]

...
-----------------------------------------------
Ashtekar wrote a review paper and a faq recently:

http://arxiv.org/abs/0705.2222

He also wrote an interesting introductory paper:

http://arxiv.org/abs/gr-qc/0702030

---------------------------------------------------------------------------------

Christine is right. I think those two recent Ashtekar papers are a good place to start, especially the introductory one: Introduction to LQG by way of LQC.

It is pedagogically smart to introduce LQG by way of its application to cosmology, because it is more concrete and hands-on.

Also you can work back---start with 2007 papers and their references will point to earlier.

Actually I am surprised that you say there is no one in Brazil doing QG.

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

Bojowald gave a series of talks in Rio de Janeiro last year (August and September 2006)

# Singularities and Quantum Gravity: V. Semiclassical Pictures
XIIth Brazilian School of Cosmology and Gravitation, 9/22/2006
CBPF, Rio de Janeiro, Brazil

# Singularities and Quantum Gravity: IV. Loop Quantum Cosmology
XIIth Brazilian School of Cosmology and Gravitation, 9/21/2006
CBPF, Rio de Janeiro, Brazil

# Singularities and Quantum Gravity: II. Beyond General Relativity
XIIth Brazilian School of Cosmology and Gravitation, 9/19/2006
CBPF, Rio de Janeiro, Brazil

# Singularities and Quantum Gravity: I. Classical Singularities
XIIth Brazilian School of Cosmology and Gravitation, 9/18/2006
CBPF, Rio de Janeiro, Brazil

# Mathematical Issues in Loop Quantum Cosmology
International Congress of Mathematical Physics, 8/08/2006
Rio de Janeiro, Brazil

I wonder who in Brazil was so interested in Quantum Cosmology as to invite him to come and give the talks, and who was
attending those talks? Maybe there is a website that lists the participants.

BTW Did you look at the Loops 07 conference program and list of participants?
http://www.matmor.unam.mx/eventos/loops07/
A sample of the core talks would give an overview of what is active in QG

 

[jvdornas]

Thanks

Yes.
I took topology off your list. It is good to study but for most current QG you don't need a deep background in it. What you do need you will be able to pick...:-)

Marcus, thank you for your attention. Some books I had acquired already, but with your reply I can study with more orientation. I am planning my studies for the next two years and I will include those disciplines. I hope I can introduce myself to LQG afterwards.

best,

JvDornas

 

[ccdantas]

Marcus,

BTW, just from what I know, I count 3 students interested in working with LQG (or non-pertubative approaches to quantum gravity) here in Brazil. This year I have been forwarded from Perimeter Institute two students interested in LQG, who contacted some researchers there, who in turn forwarded them to me; and there is another one who will be finishing his PhD in another topic and is looking for a postdoc in LQG in a near future.

As far as I can tell, there is no one here in Brazil specialized in this area, but interest seems to be growing. I've been trying to forward the students to the best places here in Brazil, that is, to experienced people who work in related areas, so that at least they can build a strong basis for future research in LQG.

However, in a near future, students willing to start a MSc or PhD program in LQG here in Brazil will hopefully have the option to enroll at http://www.ita.br/ingles/ingles.htm" . I have just started a collaboration there, so I hope to have a more concrete research line sometime soon. I hope this project finds a nice start. But for the moment, it is just a project. I'll let you know how it goes.

 

[jvdornas]

Thanks

Oi João! ...

Christine

Hi Christine,

nice to talk to you again. I had seen some books you told me already. But now with your suggestion I can guide myself better. I am anxious to start studing LQG, but I will have to wait more yet.

Thank you.

jvDornas

 

[ccdantas]

Hi João,

You can also see my (neglected ) thread here:

https://www.physicsforums.com/showpost.php?p=1355684&postcount=1

If you can travel to João Pessoa, go there and try to talk to Perez!

Best
Christine

 

[ccdantas]

I wonder who in Brazil was so interested in Quantum Cosmology as to invite him to come and give the talks, and who was
attending those talks? Maybe there is a website that lists the participants.

Surely there are many theoretical physicists in Brazil interested in quantum cosmology/gravity, but that is not to say that you will find here a clear research group or researcher in LQG (or other non-pertubative approaches to quantum gravity).

I also could not find the list of participants on that conference...

Christine

 

[marcus]

Hi João,

You can also see my (neglected ) thread here:

https://www.physicsforums.com/showpost.php?p=1355684&postcount=1

If you can travel to João Pessoa, go there and try to talk to Perez!

Best
Christine

Alejandro Perez! A collaborator of Rovelli at Marseille.
He was postdoc with Ashtekar at Penn State. now he must be junior faculty at marseille. he would be a good person to talk to

Third International Conference on Fundamental Interactions

August 6-12 2007 João Pessoa, Brazil

http://www.fisica.ufpb.br/ICFI2007/

(Charming northeastern Brazilian city with great beaches, I can tell you, almost all my relatives live there, and I have been there many, many times before...)

And among the various courses...:

-- Introduction to loop quantum gravity and spin foam models (A. Perez) Great!

Don't know whether I'll be able to attend, though...

Christine

Now I see your post, Christine. I regret having neglected it earlier
https://www.physicsforums.com/showthread.php?p=1355684#post1355684

just now I cannot get the ICFI link to work

But I can get this to work:
http://www.fisica.ufpb.br/?p=viewInform&id=1

And THIS! this is the good one for ICFI, for me:
http://www.fisica.ufpb.br/eventos/ICFI2007/

The person giving the QG SEMINAR is a Brazilian from CBPF
Nelson Pinto-Neto
Subject: Actual development in Quantum Cosmology

The danger is that Pinto-Neto might have a highly idiosyncratic approach (perhaps a different idea of quantum mechanics based on de Broglie and Bohm) so he might not give a comprehensive balanced view of current developments. But on the face of it, the seminar should be valuable: I think that quantum cosmology is the best point of entry to quantum gravity

In any case they have invited a LQG/SF expert, Alejandro Perez, to give the main talk about QC. Some of the organizers must be interested in the Loop/spinfoam approach to it.

I had a look at Pinto-Neto's two most recent papers

1) An Inflationary Non-singular Quantum Cosmological Model.
http://arxiv.org/abs/0707.1088

2) A Non inflationary model with scale invariant cosmological perturbations.
http://arxiv.org/hep-th/0610205

 

[ccdantas]

Hi again Marcus,

I have been forwarding Brazilian students interested in LQG to the following researchers here:

José G. Pereira (IFT/Unesp)
http://www.ift.unesp.br/users/jpereira/articles.html

Nelson Pinto Neto (CBPF)
http://portal.cbpf.br/index.php?page=DadosPessoa&pessoa=39

They do not work directly with LQG but in somewhat related areas.

Christine

 

[ccdantas]

But I can get this to work:
http://www.fisica.ufpb.br/?p=viewInform&id=1

And THIS! this is the good one for ICFI, for me:
http://www.fisica.ufpb.br/eventos/ICFI2007/

Thanks! They seem to have changed the link since I have posted it.

 

[marcus]

There's been a lot of progress in LQG since 2007, when this thread was written, but I notice that people still consult this thread, so we should update it. Christine you may be best able to do that.

Rovelli re-did his Living Reviews review article in 2008. So we should have a link to that.
http://relativity.livingreviews.org/Articles/lrr-2008-5/

For me, the best introductory overview is the talk he gave to the Strings 2008 conference. There's a video, and you can also download PDF of his slides for that talk and look at them in parallel with watching the video if you want, or refer to them later to help recall what he said.
The questions from the stringtheorist audience (the hall was packed!) and his answers are also worth listening to.
http://cdsweb.cern.ch/record/1121957?ln=en
http://indico.cern.ch/getFile.py/access?contribId=30&resId=0&materialId=slides&confId=21917

I will add more source material as it occurs to me. Others are invited to as well.

 

[ccdantas]

Hi Marcus,

Yes, you are certainly right. This thread is interesting in its own right: how do absolute newcomers start in (loop-canonical-covariant-...) quantum gravity? This is such a dynamic field... I have been following the latest developments and there are so much, so much, happening these past months that it is quite difficult to follow. In that respect, you have been doing a very useful job in pointing out recent papers and trends at other threads. So if you would like to add new links here, please do it!

Today, after following my own studies, I would change somewhat the approach that I have indicated in my "basic curriculum", but it's part of learning -- I was a newcomer in 2005, wrote that list one or two years later, and now, after four years (although far from a full dedicated time to it), there is still a lot of work ahead. But I am also following my own path, so... it's harder...

In very general terms, the most important point for the newcomer, I guess, is that this is a *very* dynamic field, changing rapidly, so what really matters in fact is to have a strong background, specially in general relativity and quantum field theory. Follow the arxiv everyday, have an open mind, and perhaps focus in a couple of appraches that appear interesting to you... Updates are necessary to my list, but I don't know if I'll be able to do them in a near future... I'm not saying that that basic curriculum has many flaws, but should be improved... So others are certainly very welcomed to add their advices!


Christine

 

[ccdantas]

BTW, for the *absolute beginner* in quantum gravity, Penrose's 'opus' -- "A Road to Reality" -- is the absolute warm-up, chapter zero. Highly indicated.

 

[ccdantas]

As a quick note to my basic curriculum, I'd promptly add there "Quantization of Gauge Systems" by Henneaux and Teitelboim.

And keep an eye on the upcoming book edited by Oriti -- some contributions were posted on the arxiv, and discussed here at another thread.

More on books here:

http://egregium.wordpress.com/2008/01/17/list-of-books-on-quantum-gravity-and-other-helpful-tips/

See also this:

http://egregium.wordpress.com/2008/02/10/introduction-to-lqg/

 

[ccdantas]

As a quick note to my basic curriculum, I'd promptly add there "Quantization of Gauge Systems" by Henneaux and Teitelboim.

And keep an eye on the upcoming book edited by Oriti -- some contributions were posted on the arxiv, and discussed here at another thread.

More on books here:

http://egregium.wordpress.com/2008/01/17/list-of-books-on-quantum-gravity-and-other-helpful-tips/

See also this:

http://egregium.wordpress.com/2008/02/10/introduction-to-lqg/