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Smolin's Scientific American article on LQG

  1. Sep 8, 2010 #1

    bcrowell

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    I would like to step up from the pop-sci level of understanding LQG to something more like a real physicist's understanding, but one thing that's hanging me up is the SU(2) stuff, which I don't understand, even at a hand-wavy level. Falling back to the pop-sci level to regroup, I remembered that Lee Smolin had an article on LQG, "Atoms of Space and Time," Scientific American, Jan 2004. Its discussion of spin foams is actually more detailed than in his pop-sci book Three Roads to Quantum Gravity. In the diagrams in the paper, the nodes and lines are labeled with integers representing volumes and areas. How would those integers relate to the SU(2) stuff?

    [EDIT] After posting the above, I found this, which seems to help a lot: http://math.ucr.edu/home/baez/foam/

    [EDIT] This paper by Smolin is also helping me to understand the Baez talk: http://xxx.lanl.gov/abs/gr-qc/9702030
     
    Last edited: Sep 8, 2010
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  3. Sep 8, 2010 #2

    marcus

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    The first 10 slides are a gem. They give concise clear explanation with simple examples, for anyone with a few basic linear algebra concepts (a finite dimensional vectorspace V and its dual V*, a group representation p and its dual p*, tensor product of two vectorspaces, and very little else!) Only two or three sentences per slide, and a simple picture. Baez makes it soooo simple!

    I saw those some years back and forgot what a valuable resource those few slides represent, thank for posting the link.

    The three other slides in the set don't seem as self-explanatory--they need the lecturer talking. Also they might like to be brought up-to-date (now that the Barrett-Crane spinfoam vertex formula has been replaced a revised vertex formula due to people with initials EPRL-FK.) But the first ten are a great way into the spin-network/spinfoam idea.

    Just ten little JPGs :biggrin:
    http://math.ucr.edu/home/baez/foam/foam01.jpg
    http://math.ucr.edu/home/baez/foam/foam02.jpg
    http://math.ucr.edu/home/baez/foam/foam03.jpg
    http://math.ucr.edu/home/baez/foam/foam04.jpg
    http://math.ucr.edu/home/baez/foam/foam05.jpg
    http://math.ucr.edu/home/baez/foam/foam06.jpg
    http://math.ucr.edu/home/baez/foam/foam07.jpg
    http://math.ucr.edu/home/baez/foam/foam08.jpg
    http://math.ucr.edu/home/baez/foam/foam09.jpg
    http://math.ucr.edu/home/baez/foam/foam10.jpg
     
    Last edited: Sep 8, 2010
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