= Two reduced octet matrix elements
{title2=$\langle B_r|V_i|B_s\rangle=Dd_{ris}+iFf_{ris}$}
An octet operator between <baryon octet> states has two <reduced matrix elements>, because the <tensor square of the SU(3) adjoint representation> contains two octets. The symmetric invariant $d_{ris}$ and antisymmetric invariant $f_{ris}$ give independent component tensors. Equivalently, represent baryons by traceless matrices $B$ and let the operator act as $F[t_i,B]+D(\{t_i,B\}-\tfrac23\operatorname{tr}(t_iB)I)$. Normalization choices are absorbed into $F,D$; Hermitian operators permit real coefficients in a Hermitian octet basis.
Back to article page
