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\end{eqnarray}  We replace $G^{<}_{\gamma\beta}(\omega+\epsilon) = 2i \sum_{\nu\mu} G^{r}_{\gamma\nu}(\omega+\epsilon)\Gamma_{\nu\mu}(f_{e}(\omega+\epsilon)+f_{h}(\omega+\epsilon))G^{a}_{\mu\beta}(\omega+\epsilon)$, then  \begin{eqnarray}  && \begin{aling*}  &  P^{>,3}(\omega)= \frac{4 e^2}{\hbar^2} \int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{\beta\gamma\alpha\delta\tau\theta\nu\mu} G^r_{\beta \alpha}(\epsilon) \Gamma_{\alpha\delta} G^a_{\delta \gamma}(\epsilon) [-i\Gamma_{\gamma\tau}] G^{r}_{\tau\nu}(\omega+\epsilon)\Gamma_{\nu\mu} G^{a}_{\mu\theta}(\omega+\epsilon) [i\Gamma_{\theta\beta}]\\ \nonumber && &  [(1-f_{e}(\epsilon))+(1-f_{h}(\epsilon))] [f_{e}(\epsilon+\omega)+f_{h}(\epsilon+\omega)] \end{aling*}  \end{eqnarray}  \begin{eqnarray}  &&P^{>,4}(\omega) \begin{aling*}  &P^{>,4}(\omega)  = \frac{4e^2}{\hbar^2} \int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{\beta\gamma\alpha\delta} G^r_{\beta \alpha}(\epsilon) \Gamma_{\alpha\delta} G^a_{\delta \gamma}(\epsilon) \Gamma_{\gamma\tau} G^{a}_{\tau\theta}(\omega+\epsilon) [i\Gamma_{\theta\beta}]\\ \nonumber &&\times[(1-f_{e}(\epsilon))+(1-f_{h}(\epsilon))] &\times[(1-f_{e}(\epsilon))+(1-f_{h}(\epsilon))]  f_{h}(\epsilon+\omega) \end{aling*}  \end{eqnarray}  Now we collect $P^{>,2}(\omega)+P^{>,4}(\omega)$  \begin{eqnarray}