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\end{eqnarray}  \begin{eqnarray}  &&N(\omega)=(e^2/h)\sum_{k\beta,q\gamma, N(\omega)&=&(e^2/h)\sum_{k\beta,q\gamma,  \nu\mu} \int \frac{d\epsilon}{2\pi} [G_{\beta\nu}^r(\omega+\epsilon) V_{\nu q} g^{>}_{q}(\omega+\epsilon) V^*_{\gamma q} G_{\gamma\mu}^r(\omega) V^*_{\mu k} g^{<,h}_{k}(\omega) V_{\beta k}]   &&  \\ \nonumber [G_{\beta\nu}^r(\omega+\epsilon) &&[G_{\beta\nu}^r(\omega+\epsilon)  V_{\nu q} g^{>}_{q}(\omega+\epsilon) V^*_{\gamma q} G_{\gamma\mu}^<(\omega) V^*_{\mu k} g^{a,h}_{k}(\omega) V_{\beta k}]&&  \\ \nonumber [G_{\beta\nu}^>(\omega+\epsilon) &&[G_{\beta\nu}^>(\omega+\epsilon)  V_{\nu q} g^{a}_{q}(\omega+\epsilon) V^*_{\gamma q} G_{\gamma\mu}^r(\omega) V^*_{\mu k} g^{<,h}_{k}(\omega) V_{\beta k}]&&  \\ \nonumber [G_{\beta\nu}^>(\omega+\epsilon) &&[G_{\beta\nu}^>(\omega+\epsilon)  V_{\nu q} g^{a}_{q}(\omega+\epsilon) V^*_{\gamma q} G_{\gamma\mu}^<(\omega) V^*_{\mu k} g^{a,h}_{k}(\omega) V_{\beta k}] \end{eqnarray} \end{eqnarray  Inserting the expressions for the self-energies we get  \begin{eqnarray}  N(\omega)&=&(e^2/h)\sum_{k\beta,q\gamma, \nu\mu} \int \frac{d\epsilon}{2\pi}   [G_{\beta\nu}^r(\omega+\epsilon) \Sigma_{0,\nu\gamma}^>(\omega+\epsilon) G_{\gamma\mu}^r(\omega) \Sigma_{0,\mu\beta}^{<,h}(\omega+\epsilon)]   \\ \nonumber  &&[G_{\beta\nu}^r(\omega+\epsilon) \Sigma_{0,\nu\gamma}^>(\omega+\epsilon) G_{\gamma\mu}^<(\omega) \Sigma_{0,\mu\beta}^{a,h}(\omega+\epsilon)]   \\ \nonumber  &&[G_{\beta\nu}^>(\omega+\epsilon) \Sigma_{0,\nu\gamma}^a(\omega+\epsilon) G_{\gamma\mu}^r(\omega)\Sigma_{0,\mu\beta}^{<,h}(\omega+\epsilon)]   \\ \nonumber  &&[G_{\beta\nu}^>(\omega+\epsilon) \Sigma_{0,\nu\gamma}^a(\omega+\epsilon) G_{\gamma\mu}^<(\omega) \Sigma_{0,\mu\beta}^{a,h}(\omega+\epsilon)]   \end{eqnarray