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