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SU(3), U(1), O(3), etc what are they?

  1. Aug 15, 2005 #1
    I've heard them used before...some sort of symmetry, but I never figured out what it really is. Can someone please explain the concepts to me? thx
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  3. Aug 15, 2005 #2


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    Last edited by a moderator: May 2, 2017
  4. Aug 15, 2005 #3


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    SU(3) is the "special unitary group of order 3": 3 by 3 complex matrices with determinant 1

    O(3) is the "orthogonal group of order 3": 3 by 3 real matrices with determinant 1 or -1

    U(1) is a bit puzzling! I would interpret U(n) as the "unitary group of order 3": n by n complex matrices with determinant 1 or -1. But "1 by 1 matrices" are just numbers. I guess U(1) would be the multiplicative group with members 1, -1, i, and -i!
  5. Aug 15, 2005 #4
    You will here them used to describe different types of standard model features.

    U(1) corresponds to photon
    SU(2) to W's and Z's
    SU(3) to the gluons.
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