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I Lie Algebra in Particle Physics simplified

  1. Nov 6, 2016 #1
    Hello! Is there any rule to do sums and products like the one in the attached picture (Lie.png) without going through all the math theory behind? I understand the first (product) and last (sum) terms, but I am not sure I understand how you go from one to another.
    Thank you!

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  2. jcsd
  3. Nov 6, 2016 #2


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    You can split product representations into irreps by using Young tableaux, but I do suggest you learn the theory behind it and why it works.
  4. Nov 6, 2016 #3


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    especially with SU(2)'s you can just add spins...
    2= spin 1/2
    3= spin 1
    and then seeing the multiplicity of the final spins

    Eg your example has 3 spin 1/2 particles, so you'd get something like:
    (1/2 1/2) 1/2 = ( 1 0 ) 1/2 = (1 1/2) (0 1/2) = 3/2 1/2 1/2
    so a 4 2 2
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