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B Matrices of su(3) and sphere symmetry

  1. Oct 31, 2016 #1
    i used to get pauli matrices by the following steps
    it uses the symmetry of a complex plane sphere i guess so..?
    however i cant get the 8 gell mann matrices
    please help !!

    method*: (x y) * (a b / c d ) = (x' y')
    use |x|^2 + |y|^2 = |x'|^2 + |y'|^2
    and |x| = x * x(complex conjugate)

    this way i can get 3 pauli matrices
    however can't apply them to su(3) ones..
  2. jcsd
  3. Oct 31, 2016 #2


    Staff: Mentor

    The Pauli matrices are elements of ##SU(2)## and span ##\mathfrak{su}(2)##. A (random) coincidence.

    The Gell-Mann matrices are not elements of ##SU(3)##. They span ##\mathfrak{su}(3)##.
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