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\end{equation}  We can split $Q^>(\omega)$ in four contributions  \begin{align*}  &Q^{>,1}(\omega) = \frac{ 4e^2}{\hbar^2}\sum_{k\beta,q\gamma,\alpha\mu\nu\tau,\delta\lambda} \int \frac{d\epsilon}{2\pi}[-i\Gamma_{\beta\alpha}]G_{\alpha\delta}^r(\epsilon)\Gamma_{\delta\lambda} G_{\lambda\gamma}^a(\epsilon) [-i\Gamma_{\gamma\tau}]G_{\tau\mu}^r(\omega+\epsilon)\Gamma_{\mu\nu} G_{\nu\beta}^a(\omega+\epsilon)// G_{\nu\beta}^a(\omega+\epsilon)\\  &((1-f_h(\epsilon)+(1-f_e(\epsilon)))(f_e(\omega+\epsilon)+f_h(\omega+\epsilon))  \end{align*}