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\begin{equation}  \Sigma^{r,e}_{\alpha\delta}(\epsilon) = -i\Gamma_{\alpha\delta}(\epsilon),\quad \Sigma^{a,e}_{\alpha\delta} = i\Gamma_{\alpha\delta}(\epsilon)  \end{equation}  Similar equations are hold for $\Sigma^>$ $\Sigma^{>,e }(\epsilon)= 2i [1-f_{e}(\epsilon)] \Gamma_{\alpha\delta}(\epsilon)$ and$\Sigma^{>,h}(\epsilon)= 2i [1-f_{h}(\epsilon)] \Gamma_{\alpha\delta}(-\epsilon)$. Then,  \begin{eqnarray}  &&S^{>,1}(\omega)= \frac{e^2}{\hbar^2}\int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{\beta\gamma\alpha\delta} G^r_{\beta \alpha}(\epsilon) \Sigma^>_{0,\alpha\delta}(\epsilon) G^a_{\delta \gamma}(\epsilon)\Sigma^{h,<}_{0,\alpha\delta}(\epsilon+\omega) \\ \nonumber  && = 2 i \frac{e^2}{\hbar^2}\int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{\beta\gamma\alpha\delta} G^r_{\beta \alpha}(\epsilon) [ (1-f_{e}(\epsilon)) \Gamma_{\alpha\delta}(\epsilon) + (1-f_{h}(\epsilon)) \Gamma_{\alpha\delta}(-\epsilon)] G^a_{\delta \gamma}(\epsilon) f_{h}(\epsilon) \Gamma_{\alpha\delta}(-(\epsilon+\omega))]  \end{eqnarray}