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Loop Quantum Gravity?

  1. May 7, 2008 #1
    I understand that it is a quantum take on space-time. I just don't actually understand IT. Can anyone help? Any good online lectures or explanations?

  2. jcsd
  3. May 7, 2008 #2
    "Marcus" has posted a lot of good links in the "Beyond the Standard Model" forum.

    What I recommend is trying to find Carlo Rovelli's "Quantum Gravity" textbook, or trying to read Lee Smolin's old Arxiv postings (See here or here or here, maybe?) There is unfortunately not one canonical introduction to LQG (though Rovelli's book maybe comes close?) but if you read a few papers on the subject you'll probably get the general direction.

    It will help to know some differential geometry, and John Baez's "this week in mathematical physics" series contains a lot of good information about the background math. (Baez also wrote a book on the loop formalism and there's stuff about spin networks and spinfoams littered all over his website.)
  4. May 7, 2008 #3


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    It depends on your background. Do you have a solid background in QFT?
  5. May 7, 2008 #4
  6. May 7, 2008 #5


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    Check out this recent thread for many online lectures

  7. May 7, 2008 #6
    In case you're interested in something a bit more substantial than online lectures you might find the following of help. Rovelli's book is a good read, dealing, as it does, with many of the basic topics. It should be noted, however, that it's philosophical in nature, and most certainly isn't a textbook. I also have severe disagreements with several points he raises in the book (indeed, he makes more than a few claims which are patently false). Nonetheless, it's worthwhile getting hold of a copy if you're serious about learning this stuff.

    A more comprehensive book is Thiemann's Modern Canonical Quantum General Relativity. It's comprehensiveness comes at a significant price though: it's much more appropriately viewed as a reference work and not as a textbook. Thiemann has an annoying habit of using terribly nonstandard notation in places but his presentation of the material is usually superb. There's also a large number of useful appendices if you need to brush up on your differential geometry, topology, and so on.

    My personal favourites are the following three:

    • Baez & Muniain, Gauge Theories, Knots, and Gravity;
    • Ashtekar, Lectures on Nonperturbative Canonical Gravity;
    • Kiefer, Quantum Gravity.

    Of the three, Baez & Muniain is certainly the most readable. If you're familiar with Baez's This Week's Finds... series you'll know he has a particular talent for apposite, chatty, and insightful explanations, something which shines through in this book. It may perhaps be the best introduction to the area.

    Ashtekar's book is pitched at a considerably higher level. In particular, he dives straight into a discussion of the new variables, so if you're not familiar with this material you'll need to learn this first. Still, it's a book that everyone who works in the area has/should have.

    Kiefer's book is my personal favourite. It's not restricted solely to LQG (although his discussion of this is very good; he also covers Regge calculus and dynamical triangulations, black holes and quantum cosmology, and a cursory treatment of string theory. His discussion of the Hamiltonian approach (which is what you're really interested in when looking at LQG) is superb, cutting out much of the extraneous and irrelevant material that you'll find in, for example, Rovelli's book.

    Hope that's of help.
  8. May 7, 2008 #7


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    I'd be interested in hearing more about what he says that is false.
  9. May 7, 2008 #8
    Pretty much his whole line of thinking about Kretschmann's objection to general covariance is shaky, as is his discussion of the nature of time in relation to the substantivalist/relationist debate about the structure of spacetime. Those are two rather fundamental issues off the top of my head.

    His treatment of the problem of time in canonical QG is also particularly weak. It certainly pales in comparison to the early work of Isham, Kuchar, and others.
    Last edited: May 7, 2008
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