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\end{eqnarray}  They can be reformulated in terms of self-energies as  \begin{eqnarray}  S^{>,1}(\omega)= \frac{e^2}{\hbar^2}\int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{k,q,p\beta\gamma\alpha\delta} \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) \end{eqnarray}  \begin{eqnarray}  S^{>,2}(\omega) = \frac{e^2}{\hbar^2} \int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{k,q,p\beta\gamma\alpha\delta} \sum_{\beta\gamma\alpha\delta}  G^r_{\beta \alpha}(\epsilon) \Sigma^>_{0,\alpha\delta}(\epsilon) G^a_{\delta \gamma}(\epsilon) \Sigma^{h,r }_{0,\gamma\gamma}(\epsilon+\omega) G^{r}_{\gamma\beta}(\omega+\epsilon) \Sigma^{h,<}_{0,\beta\beta}(\epsilon+\omega) ] \end{eqnarray}  \begin{eqnarray}  S^{>,3}(\omega)= \frac{e^2}{\hbar^2} \int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{k,q,p\beta\gamma\alpha\delta} \sum_{\beta\gamma\alpha\delta}  G^r_{\beta \alpha}(\epsilon) \Sigma^>_{0,\alpha\delta}(\epsilon) G^a_{\delta \gamma}(\epsilon) \Sigma^{h,r }_{0,\gamma\gamma}(\epsilon+\omega) G^{<}_{\gamma\beta}(\omega+\epsilon) \Sigma^{h,a}_{0,\beta\beta}(\epsilon+\omega) ] \end{eqnarray}  \begin{eqnarray}  S^{>,4}(\omega)= \frac{e^2}{\hbar^2} \int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{k,q,p\beta\gamma\alpha\delta} \sum_{\beta\gamma\alpha\delta}  G^r_{\beta \alpha}(\epsilon) \Sigma^>_{0,\alpha\delta}(\epsilon) G^a_{\delta \gamma}(\epsilon) \Sigma^{h,< }_{0,\gamma\gamma}(\epsilon+\omega) G^{a}_{\gamma\beta}(\omega+\epsilon) \Sigma^{h,a}_{0,\beta\beta}(\epsilon+\omega) ] \end{eqnarray}  Now we explicitely write down the expressions for the self-energies  \begin{equation}  \Sigma^>_{0,\alpha\delta}(\epsilon) = \Sigma^{>,e}_{0,\alpha\delta}(\epsilon)+\Sigma^{>,h}_{0,\alpha\delta}(\epsilon)  \end{equation}  with   \begin{equation}  \Sigma^{>,e}_{0,\alpha\delta}(\epsilon) = 2 i f(\epsilon-\mu_N)\Gamma_{\alpha\delta}(\epsilon)  \end{equation}  and  \begin{equation}  \Sigma^{>,h}_{0,\alpha\delta}(\epsilon) = 2 i f(\epsilon+\mu_N)\Gamma_{\alpha\delta}(-\epsilon)  \end{equation}  On the other hand we have for the retarded and advanced self-energies  \begin{equation}  \Sigma^{r,h}_{\alpha\delta}(\epsilon) = -i\Gamma_{\alpha\delta}(-\epsilon),\quad \Sigma^{a,h}_{\alpha\delta} = i\Gamma_{\alpha\delta}(-\epsilon)  and   \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}