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How to find 3D representation of SU(2)

  1. Jun 6, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the 3D representation of what I think are the commutators [T_a,T_b] for the SU(2) group


    2. Relevant equations

    I think the generators(X_i) in SU(2) group are the 3 Pauli matrices, which are 2X2 matrices... I assume I need to find the matrices for these generators as 3x3?

    3. The attempt at a solution

    I think the equation exp^(i*alpha_i*X_i) determines what the elements of the group are...
    [T_a,T_b)=T_a*T_b - T_b*T_a is the commutator
    Since there are 3 generators, does that also mean there should be three matrices in 3X3 representation?

    Do I sound confused???? :cry:
     
  2. jcsd
  3. Jun 6, 2013 #2
  4. Jun 6, 2013 #3
    A huge thanks to you, sgd37!! No more tears!!
     
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