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SU(3) from three belts?

  1. Apr 29, 2009 #1
    Dear PFers,

    I am looking for a way to visualize SU(3). I have heard from a friend
    (who heard it as a rumor) that like SU(2) can be
    visualized with a (Dirac) belt, also SU(3) can be visualized, but
    with three belts, because SU(3) has three independent copies of
    SU(2) as subgroups.

    I found no material on this on the internet.
    Is there anybody who can help me with more details? Thank you!

    Franca
     
  2. jcsd
  3. Apr 29, 2009 #2
    Hi Franca,

    the only place I have seen something similar is the last manuscript
    on http://www.motionmountain.net/research [Broken]
    where Schiller uses the triple belt trick to model the strong
    interaction. Does this help you?

    François
     
    Last edited by a moderator: May 4, 2017
  4. Apr 29, 2009 #3

    tom.stoer

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    Science Advisor

    what's the Dirac belt?
     
  5. Apr 29, 2009 #4

    apeiron

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    Gold Member

    Penrose used the single belt in a book to illustrate SU2 and spinor symmetry on around p200 of his Road to Reality from memory. Maybe your friend saw those pictures?

    But not come across a three belt illustration of SU3.

    The 1 belt trick is also illustrated on p21 of this paper...
    http://website.lineone.net/~cobble6/Clifford Report.pdf
     
  6. Apr 29, 2009 #5
    Thank you, that preprint is very interesting! I wanted the three
    belts to understand nuclei, but that manuscript does something
    much more ambitious: it tries to derive QED, QCD and QAD from
    topologocal arguments. Incredible!

    Franca

    P.S. I very much like this (single) belt trick applet:
    http://gregegan.customer.netspace.net.au/APPLETS/21/21.html
     
    Last edited by a moderator: May 4, 2017
  7. Apr 30, 2009 #6

    tom.stoer

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    Science Advisor

    thanks - now I remember
     
  8. May 3, 2009 #7
    In the meantime, I asked a bit around. The three belt idea is not
    well-known yet. Searching for "three belts" and "SU(3)" gives
    no hits anywhere. the manuscript above is a bit terse on
    the topic, probably because the main topic is unification.

    The main idea is that SU(3) has three copies of SU(2)
    that are linearly independent. Each SU(2) can be modelled
    by one belt. So three copies need three belts.
    Then the three belts are connected by joints.

    The 8 generators of SU(3) are explained as rotations by 180
    degrees; and their products are said to be concatenations.
    But though I can deduce some of the products, I fail
    for others.

    Did anybody else try?

    Franca
     
    Last edited by a moderator: May 4, 2017
  9. May 5, 2009 #8
    I have tried a few products, and it seems to work out. The rest of the
    file is more intriguing: the guy is going for the holy grail
    of physics... It is quite a change in approach to what is seen around.
    Unification in 3 d , unusual SU(2) symmetry breaking proposal, no GUT, non Susy - that is not the usual stuff...

    François
     
  10. May 6, 2009 #9
    I asked about this on usenet. It seems to me that the approach has a chance.
    I will post more on this approach to unification once I have made up my mind.

    Franca
     
  11. May 8, 2009 #10
    On sci.physics.research, Heinz posted this assessment:

    --------

    Franca, tell me if I write too much or too little. Here is what I get
    from that text. It has 2 claims.
    One is mathematical. It claims that the first Reidemeister move (that
    is a standard way to deform knots)
    is a generator of U(1), the second move(s) gives the generators of SU
    (2), and the third Reidemeister
    moves gives the generators of SU(3). See the wikipedia entry
    http://en.wikipedia.org/wiki/Reidemeister_move .
    *IF* the connection is correct, then the answer to
    your question is that the gauge groups can indeed be related/tied to 3
    dimensions.
    The opposite is true if the claim is wrong. But even if the claim is
    correct,
    this does not mean that the physical gauge groups (as opposed to the
    mathematical groups)
    really are due to 3 dimensions. Other explanations are possible:
    string theory.
    So the answer to your question is: "maybe."

    The other claim is physical: Schiller claims that particles are
    tangles, and that
    Reidemeister moves model gauge interactions. That can only be tested
    against experiment. Schiller says that tangles lead to the Dirac
    equation, and
    gives a published paper from 1980 as a proof, plus an unpublished text
    by himself.
    *IF* the reasoning is correct, test with experiment would not be
    necessary: it is
    known that the Dirac equation is very precise.
    The opposite is true if the reasoning is wrong. The 1980 paper appears
    to
    have almost no citations. So the answer to this claim is "hmm".
    Does this answer your question?

    Heinz

    ------

    I will read the 1980 paper and more on Reidemeister things and come back soon.

    Franca
     
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