 Two reduced octet matrix elements

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 $F[t_i,B]+D(\{t_i,B\}-\frac{2}{3}\mathrm{tr}(t_{i}B)I)$. Normalization choices are absorbed into $F,D$; Hermitian operators permit real coefficients in a Hermitian octet basis.