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Baez and Schreiber paper on 2-bundles

  1. Dec 30, 2004 #1


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    This was announced today at SPS and coffeetable:

    John Baez & Urs Schreiber,
    Higher Gauge Theory: 2-Connections on 2-Bundles

    quote from abstract:
    "...the concept of ‘2bundle’ recently introduced by Bartels. A 2-bundle is a generalization of a bundle in which the fibers are categories rather than sets. Here we introduce the concept of a ‘2-connection’ on a principal 2-bundle..."

    might be important
    the arxiv link will not work until next week because of holidays
    but the paper (73 pages) can be downloaded from a link Urs gave

    Eric Forgy, who sometimes posts at PF, did some pictures for this paper.
    Work by Florian Girelli and Hendryk Pfeiffer is cited.
    As such things go, the paper looks comparatively readable---at least by categoriphiles.
    Last edited: Dec 30, 2004
  2. jcsd
  3. Dec 30, 2004 #2


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    Thank you, Marcus. You're on the ball as usual.

    Lubos and Urs are discussing this on .strings if anyone is interested.

    No prizes for guessing which side I'm on.
    Kea :smile:
  4. Dec 30, 2004 #3


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    the importance of categories

    One of the founders of modern category theory is F. W. Lawvere.
    In 1973 he said: ".....has led some people to attempt to characterise the philosophical significance of the theory of categories as that of a 'third level of abstraction'. But the theory of categories actually penetrates much more deeply than that attempted characterization would suggest toward summing up the essence of mathematics."

    That was in the paper
    Metric spaces, generalized logic and closed categories
    F. W. Lawvere

    But is it essential to physics? This remains to be seen. It must make falsifiable predictions that distinguish it from the alternatives. The fact that it unifies the mathematics of GR and QFT is not sufficient to call it physics.

    However, consider that something like T-duality exists in both String theory and any reasonable existing alternatives of which I am aware. This demands new physical thinking. I have asked Lubos to clarify his physical description of T-duality but he has as yet to respond.

    We await with baited breath.
  5. Dec 30, 2004 #4


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    my dear mountain parrot,
    I understand how to bait a trap and bait a hook
    but cannot imagine how one baits one's breath.

    If you mean that your breath is bated, that is
    restrained or diminished, while you await Lubos' reply,
    then I wish he may reply speedily before hypoxia occurs.

    Tell me about the type of
    New Zealand wild parrot called the Kea. I have never seen
    or heard one. I am told they are intelligent and mischievous birds.
    Is this correct?
    Last edited: Dec 30, 2004
  6. Dec 30, 2004 #5


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    Hi Marcus


    Ahh. My identity revealed. It had to happen. And thankyou for
    the English correction...though I quite like the image of impatient panting of foul breathed and unwashed nerds looking for excitement.

    The Kea is far more intelligent than human beings. Let me give you a couple of anecdotes.

    They like rubber and other chewy things because they make nice toys. There is a wilderness hut down south which gets many visitors each day in the summer. It is high on a ridge and has a large freezer door - so the Keas can't get inside. In this particular place, the Keas like to steal people's boots. They drag them (the boots being heavy mtn boots and too heavy to lift) about 100m to the edge of a 1000m high cliff and drop them off with great glee.

    Trying to warn visiting Europeans about this is sometimes futile. Some people learn the hard way.

    They often arrive in gangs - usually teenage males. I was once camping with a friend and we were kept up for many hours. Two of them were playing slippery dip on the roof (they're fond of that game), another pulling the pegs out of the ground, another trying to sneak inside whilst we were busy dealing with the others....

    Kea :smile:
  7. Jan 2, 2005 #6


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    this disquisition on Kea birds is one of the most agreeable things Ive read on PF lately.
    I like imagining one of these small parrots dragging a hiking boot (a symbol of the non-winged-ness of humans) and pushing it off a cliff (fly, boot, you ineffective substitute for wings)

    I didnt know about these birds until Kea herself showed up here and then I had to google

    well, the Baez Schreiber paper is now available on Arxiv in the usual way.

    There were a couple of other papers newly posted today as well:

    Kenneth Wilson (of Wilson loops) personal memoir on the history of Lattice Gauge Theory. he recalls a time in the 1960s when graduate students did not all cluster in the hottest areas of research but went exploring more, and he is a great respecter of crazysounding offbeat ideas. he says you have to encourage eccentric research pursuits. I guess Richard Feynman made a speech about that, emphasizing the risk of scanty rewards for doing that, but also the necessity if the enterprise as a whole is to thrive.
    Well, Wilson has a modest moral sermon mixed in with entertaining anecdotes and real life story.

    and then there is another update by Giovanni Amelino Camelia on
    QUANTUM GRAVITY PHENOMENOLOGY, that he just posted today.
    He has written a series of such reviews of the current state of QG Phenom. and I hope the current state is getting better or at least changing.

    I wont bother to give the arxiv number because anyone who wants can use the search tool with the author name.
  8. Jan 3, 2005 #7
    Kea are also the most amazing shade of green. They look like little parrots only a lot bigger.

    If you ever head over the Arthurs Pass in the Sth Island and stop on the lookout they will just come over and start shredding anything you walk away from.

    I like them
  9. Jan 3, 2005 #8


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    It appears that I have been banned from .strings. Cool! That wasn't hard.

    How about this one? Keas can slide bolts on doors. Once they locked two guys in a hut, and it took them most of the day to get out.
  10. Jan 4, 2005 #9


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    Urs Schreiber and Lubos are continuing to debate this matter on .strings, but I'm afraid that this particular point will have to be made here.

    Let me try to explain this again! The paper

    Higher gauge theory - differential versus integral formulation
    Florian Girelli, Hendryk Pfeiffer

    explains the basics of 2-groups and gauge transformations. Baez and Schreiber have looked at 2-functors into 2-groups in order to understand higher holonomy. This is beautifully worked out in great detail.

    However, we know that this formalism is insufficient to cover the aspects of M-theory in question, because from M-theory one should be able to recover the mechanism for confinement and we know how this relies on tricategorical information: see references to, for instance, Joyce's work, which are given several times elsewhere on PF.

  11. Jan 4, 2005 #10


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    This might just be opinion, but until one comes to grips with the importance of Gray tensor product (this is very category theoretic) one cannot understand M-theory.

    If one accepts that strings are somehow categorified (point) particles (Schreiber's picture) then 'state spaces' should be 2-categorical, meaning that one should expect system combination to rely on Gray products.

    Non-conservation of 'particle' number is thus related to non-conservation of categorical dimension. Of course, I should be providing more details here...will do so when I can.
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