 $$\begin{aligned} \Sigma^B_{\beta j}(\textbf{q},\omega)=\hat{L}_{0 \beta \gamma j k}G_{\gamma k}^0(\textbf{q},\omega)=\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \nonumber \\ =\int \ d^0s q_{\alpha}q_{l} s_{\delta} s_{i} \tilde{R}_{\alpha \beta \gamma \delta ijkl}(\textbf{q}-\textbf{s})G_{\gamma k}^0(\textbf{s},\omega)\label{Sigma_Bo_F},\end{aligned}$$ 