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A First Course in Loop Quantum Gravity

  1. Nov 17, 2007 #1
    I am reading Barton Zwiebach's 'A First Course in String Theory'. I expect I will finish up in about a month. Not that I understand it that well. I will put it aside and perhaps read it again in a couple of years. I took a peek at the book 'String Theory in a Nutshell' by Elias Kiritsis and realized how little I absorbed on my first reading, even chapter 1 of that book is beyond me. Professor Zwiebach's book was written for Sophomores at MIT and that's why I was able to read it at all. I wonder if there is a book on Loop Quantum Gravity that is aimed toward beginners like me.
     
  2. jcsd
  3. Nov 17, 2007 #2
    Nope. There's certainly nothing comparable to the low level at which Zwiebach's book treats string theory.
     
  4. Nov 17, 2007 #3

    marcus

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    I would guess shoehorn's right there isn't, at least up to a point.
    I don't know how far you want to stretch "comparable".

    The most recent book that could be a LQG textbook at some appropriate level is Thiemann's
    which came ouit this fall and is discussed in this thread
    https://www.physicsforums.com/showthread.php?t=196209
    It's not a book for college sophomores though.

    Three PF member posting in that thread own the book, and one of them has written a review of it and posted it on his website. A fourth PF person says he has looked it over but not bought it.

    The PF posters who own the book or have looked at it and have something to say about in in that thread are
    AngryPhysicist
    geoffc
    Perturbation
    staf9

    the book tries to be mathematically selfcontained---that is it has a separate section of 200 pages which covers all the various math tools that it uses in developing LQG
    ====================

    there is an online video series with about 20 lectures by Lee Smolin (and 3 guest lecturers) called Introduction to Loop Quantum Gravity

    Google PIRSA (Perimeter Institute Recorded Seminar Archive). Some undergraduates at University of Waterloo were taking the course and the lectures were recorded. It is interesting but not consistently at undergraduate level. There were graduate students and postdocs sitting in.
    ====================

    A popular account of LQG can be found in Smolin's book Three Roads to Quantum Gravity. I was surprised by how much understanding it delivers, but it is not mathematical at all.
    ====================

    Obviously there is nothing I can think of that precisely matches Zwiebach!
     
    Last edited: Nov 17, 2007
  5. Nov 17, 2007 #4
    jimmy, if you can manage to find it, Srivastava's Supersymmetry, Superfields and Supergravity is a nice graduate text that'll get you up to speed on some of the string theory prerequisites such as: N-extended Super Yang-Mills theory, Grassmann variables and supermultiplets.
     
  6. Nov 17, 2007 #5
    And how! I bought it this morning at the CUP bookstore. First impressions: it's heavy, very heavy, and ludicrously expensive even for a CUP first printing. Apart from that, it touches most of the bases that Thiemann covered in his ArXiv review of the same topic, and then some.

    It's certainly not something that could profitably be read by an undergraduate. (And I brook no argument on this point. Undergrads may have been exposed to, say, GR but they won't have been exposed to it at anywhere near the level required to have a solid understanding of, for example, the ADM decomposition.)
     
  7. Nov 18, 2007 #6
    I read Schutz' "A FIrst Course in GR" and I feel confident on the material through chapter 8. Chapter 9 killed me. What does that tell you? I will take a look at Thiemann but I can't decide if it is right for me until I do. I see the town library has one of it's three copies still checked in. I think I better start with Smolin as I started with Brian Greene for ST. The library's copies are all checked in. After that Srivastava sounds like something I would enjoy even if just for the math. The library has this one, but it is in the depository and requires 24 hours notice before being checked out. Thanks everyone for your input so far.
     
    Last edited: Nov 18, 2007
  8. Nov 18, 2007 #7
    Jimmy you don't sound ready for Thiemann. Take a look at John Baez's book Gauge Fields, knots, and Gravity it was written as prerequisite for loop quantum gravity. I think this book is you r best bet, and it is such a great book for people with a decent knowledge of math who are not yet professionals.
     
  9. Nov 18, 2007 #8
    My impression is that one would need to be familiar with, at a bare minimum, the following topics in order to really get something out of Thiemann's book:

    0) Lie groups, Lie algebras, and canonical quantization at a formal level.
    1) Symplectic and Poisson manifolds.
    2) Van Howe and Groenewald's arguments for the incompleteness of geometric quantization.
    3) The ADM formulation of GR.
    4) Ashtekar's variables (definitely with his approach to complexified general relativity, possibly with the real approach also).

    Some may disagree with this, but that's what I'd deem necessary. If you're unsure whether you're able to understand the book, have a look at Thiemann's gr-qc/0110034. There's a not insignificant overlap between that paper and the contents of the book.

    By the way, someone else suggested John Baez's book earlier in this thread. I'd forgotten about it but it's actually a very good, very easy read; I like his style of writing a lot. If I were you I'd get a hold of that, read it while at the same time learning as much differential geometry as you can, and by the time you're done with it you'll not only be much better prepared for Thiemann, but Thiemann's book should also be out in paperback by that stage.
     
    Last edited: Nov 18, 2007
  10. Nov 18, 2007 #9
    Christine Dantas compiled a good list of resources on her old blog, http://christinedantas.blogspot.com/ - you have to scroll down to the heading "A basic curriculum for Quantum Gravity".

    In particular I recommend:
    - Carlo Rovelli's book "Quantum Gravity". This is probably more accessible than Thiemann's.
    - Lee Smolin's online lectures. These were targetted at upper year undergraduate physics students. The links are available from Christine's blog.
    - John Baez's course notes from his Quantum Gravity seminar. http://math.ucr.edu/home/baez/QG.html. This is more abstract and mathematical, but should be accessible to undergraduate math students.
     
  11. Nov 18, 2007 #10
    It's definitely more accessible than Thiemann's book and contains several interesting discussions from a conceptual standpoint, but I remain doubtful that it's accessible enough for an undergraduate. For instance, in chapter two Rovelli introduces various actions for general relativity but doesn't go into any detail regarding how the field equations can be derived from these actions. Since these actions are all vielbein-based, I'd expect a reader to have a knowledge of differential forms and their use in variational principles before being able to appreciate these points. Again, I'm not convinced that this is something a typical undergraduate would have come across.

    Nevertheless, it is a nice book.
     
  12. Nov 18, 2007 #11
    You can also check the references, bibliography & external links in Wikipedia's loop quantum gravity page. All the cross references have been checked & the whole page has been examined from a layman's point of view, but there is a need for LQG experts to review this page & bring it up to date with developments in the LQG field.
     
    Last edited: Nov 18, 2007
  13. Nov 18, 2007 #12
    Sounds like consensus. I can't even spell ADM, so I took out a copy of Professor Baez's "Gauge Fields, Knots, and Gravity". Here's what it says: "The main prerequisites are some familiarity with electromagnetism, special relativity, linear algebra, and vector calculus, together with some of the indefinable commodity known as mathematical sophistication". That defines me. I also took out a copy of Smolin's 'Three Roads'. Thank everyone for all your help. I expect I will be asking questions on the homework help forum pretty soon.
     
  14. Nov 19, 2007 #13
    I think there is no way to seriously start learning quantum gravity without a proper background: first, you need to have followed an undergraduate program in physics or mathematics.

    Then the next step would be to study the very nice book by Baez, already mentioned here. Next (or along with Baez's book) go to Frankel's book (The Geometry of Physics). I did not like it very much at first, but now I go back to it all the time and I think it is useful. Another one (somewhat more advanced than Frankel) is Nakahara's book.

    Meanwhile when you start to feel that you are ready, go for some tutorials, they are available at the arxiv (you can find some links from my old blog, as already mentioned here as well). If you find some difficulty, go back to the books above and get back to the papers, etc. Learning all that material is a nonlinear process.

    The PI lectures by Lee Smolin are advanced and have some prerequisites (as mentioned in the abstract of the course): you'll need them apart from those mentioned above. You can watch the videos and/or download the lectures (pictures of the blackboard in pdf).

    (BTW, I'm in a long and lonely journey LaTeXing those Smolin's lectures. I don't have a projection of when I'll finish them (it's a very slow process for several reasons and I might simply give up on them if my energy runs out for something else). So if there is someone else doing this, please let me know! (I asked Smolin but he does not know of anyone else LaTeXing his lectures).)

    Finally, follow the arxiv new papers everyday. PF is a nice place to keep up to date about the headings in current research. There is a lot going on and it is easy to get lost. That is a reason why it is more important to know the fundamentals than the details of things that change so rapidly and can be simply dead-ends. When you have solid understanding and maturity you can follow whatever path or idea that interests you, that is much more important than having an encyclopedic knowledge but no wisdom or truthful understanding of the underlying physics.


    Thanks,
    Christine
     
  15. Nov 19, 2007 #14
    Thanks Christine. I have a master's in math, so that's not an issue. Solid understanding still eludes me though, my maturity and wisdom are up for dispute, I certainly don't have encyclopedic knowledge and to say I had a truthful understanding of the underlying physics would be a lie. Heck, I don't even understand the superficial physics.
     
  16. Nov 19, 2007 #15
    So we are in pretty the same boat. I have a PhD in Astrophysics and I am struggling will all those issues as well!

    Good luck.
    Christine
     
  17. Nov 19, 2007 #16
    The Baez book might be too elementary for me. Here is Exercise 53, page 449:
    I have a marvelous solution for the exercise which this post is too small to contain.
     
  18. Nov 7, 2011 #17
    This book has finally released by the end of Oct, 2011.
     
  19. Nov 7, 2011 #18

    martinbn

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  20. Nov 7, 2011 #19
    I just received my copy of Gambini and Pullin's book. IMHO it's extemely well-written and gives, for an undergraduate audience, a nice meaningful flavour of some of the maths that goes into the LQG programme, without crossing the boundary where an undergrad might struggle. Even if you don't have any "faith" in the LQG approach, the first 2/3 of the book is still gives an excellent "taster" of GR, constraints, QFT, Ashtekar variables. Great for a 3rd year first degree course.
     
  21. Nov 7, 2011 #20

    atyy

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