1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Problem with SU(3) generators's trace

  1. Jul 11, 2012 #1
    Hi everyone. I'm not sure this is the correct section for this topic and if not my apologiez.
    I'm studying SU(3) and my professor wrote down the following equality:

    $$Tr\left(\left[ T^a_8,T^b_8\right] T^c_8\right)=i\frac{3}{2}f^{abc}$$

    where Ts are generators of the adjoint representation. I'm not sure this relation is correct and I would like to have your opinion. The Dynkin index of the adjoint representation is 3 so:

    $$Tr\left(T^a_8T^b_8\right)=3\delta^{ab}$$

    Now, my reasoning is:

    $$Tr\left(\left[T^a_8,T^b_8\right]\right)=if^{abd}Tr(T^d_8T^c_8)=if^{abd}3\delta^{dc}=3if^{abc}$$

    The difference is just a 1/2 factor but I would like to know if I'm doing something wrong.

    Thanks everybody
     
  2. jcsd
  3. Jul 11, 2012 #2
    The index for SU(3) should be 3 in the adjoint representaion (and N generally). You should probably ask him to clarify.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook