- #1
Einj
- 470
- 59
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
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