Flavor SU(3) Cartan generators
= Flavor SU(3) Cartan generators
{title2=$\operatorname{tr}(h_ih_j)=\delta_{ij}$}
For <flavor symmetry> acting on $(u,d,s)$, trace-orthonormal Hermitian diagonal generators are $h_1=\operatorname{diag}(1,-1,0)/\sqrt2$ and $h_2=\operatorname{diag}(1,1,-2)/\sqrt6$. The <isospin> and <flavor hypercharge> operators are $I_3=h_1/\sqrt2$ and $Y=\sqrt{2/3}\,h_2$. Their multiples by $i$ lie in the compact <SU(3) Lie algebra>.