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Diff invariance allows loop variables why?

  1. Feb 20, 2009 #1
    I don't understand why a diffeomorphism invariance allows the extention of the loops variables in the continuum limit. Can someone give me some detailed reference?
     
  2. jcsd
  3. Feb 20, 2009 #2

    marcus

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    I wasn't sure what you were asking, but it could be you would like a reference for why loop quantum gravity is UV-finite. This is basically a consequence of the theory being diffeomorphism invariant.

    Rovelli explained that to an audience of several hundred string theorists at the Strings 2008 meeting at CERN last summer. I will get the links to the PDF and the video. Actually the links are here
    https://www.physicsforums.com/showpost.php?p=2040943&postcount=143
    If you look down through that post you will come to this block of links

    Rovelli's 2008 LQG overview:
    http://relativity.livingreviews.org/Articles/lrr-2008-5/ [Broken]

    2008 LQG survey talk to the Strings '08 conference, video and slides
    http://cdsweb.cern.ch/record/1121957?ln=en
    Slides (UV finiteness discussed starting at slide #22 or 23):
    http://indico.cern.ch/getFile.py/access?contribId=30&resId=0&materialId=slides&confId=21917

    2008 LQG survey talk to Loops '08, general, slides, audio
    http://www.maths.nottingham.ac.uk/qg/wiki/index.php/QGsquared-slides [Broken]
    http://www.maths.nottingham.ac.uk/qg/wiki/images/3/3f/RovelliCarlo1214510081.pdf [Broken].

    Others of these might be useful to you as well as the LQG survey talk given to the strings conference last August. In talking to the String experts, Rovelli used a somewhat intuitive nontechnical style, because talking to nonspecialists, this I think makes the talk especially useful. Also one can see what points the audience found hard to understand and what they needed to ask questions about.

    I still am not sure about your question, so you could REPEAT the question and give a little more context. Are you talking about LQG spin networks?
    Or do I misunderstand and you are asking about something else entirely! Are you talking about UV finiteness? Clarify, if you want to.
    In the video (which is 43 minutes long) the discussion of UV finiteness starts around 17:00 minutes, when he comes to the section called Dynamics. Until today I could always get the video+audio. Today I could not get the full video right away, hope you have better luck. I had to pause it and wait for it to download a couple of minutes and then unpause it. It is an excellent talk.
     
    Last edited by a moderator: May 4, 2017
  4. Feb 21, 2009 #3
    i was refering exactly to that talk for string theorists. In presenting loop variables, rovelli said that loop variables borns in lattice theories and in the general cases you can't extend loop variables in the continuum space limit but for diff invariant theories.
    why?
     
  5. Feb 21, 2009 #4

    marcus

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    There is a nice short formal proof of finiteness on page 281 of Rovelli's book.
    (I have the hardcover first edition). He also gives some intuitive explanation to help understand why the mathematical proof works, down at the bottom of page 281.

    As he mentions on the top of page 277, the UV finiteness extends to matter fields defined on the LQG spin network, and he discusses this formally starting on page 289, section 7.3 "Matter: dynamics and finiteness"

    You asked for some references to things to read. I don't want you to have to go and buy Rovelli's book! :smile: What we need to do is find out what page 281 corresponds to in the free-online early draft version.

    The section we have to look for is called 7.1.1 "Finiteness". I think if we go back to the early draft version the page number will be different but probably the section number, 7.1.1, will be the same. At least the chapter order will be the same, so look in chapter 7.

    To find the free downloadable 2003 draft version, google "Rovelli"
    which will give you
    http://www.cpt.univ-mrs.fr/~rovelli/
    and on that page you will find a link to the free copy.
    Oh no! I just checked, and the link to the free copy has gone away! This presents a problem.
    =====ADDED LATER=======
    Whew! The book is still available free, here:
    http://www.cpt.univ-mrs.fr/~rovelli/book.pdf
    And the explanation you need is on page 202 (of the old draft version) in section 7.1.1
    Check it out! He is a clear writer who puts in a lot of intuition.
     
    Last edited: Feb 21, 2009
  6. Feb 22, 2009 #5
    thank you very much.
     
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