deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 96a2da0..7d36fb2 100644  --- a/untitled.tex  +++ b/untitled.tex 
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G^{h,>}_{k\gamma}(\omega+\epsilon) = \sum_\alpha [g^{r,h}_{k}(\omega) V_{\alpha k} G_{\alpha\gamma}^>(\omega)+g^{>,h}_{k}(\omega) V_{\alpha k} G_{\alpha\gamma}^a(\omega)]  \end{eqnarray}  \begin{eqnarray}  G^{<,h}_{q G^{<}_{q  \beta}(\omega) = \sum_\alpha [g^{r,h}_{q}(\omega) [g^{r}_{q}(\omega)  V^*_{\alpha q} G_{\alpha\beta}^r(\omega)+g^{r,<}_{q}(\omega) G_{\alpha\beta}^r(\omega)+g^{<}_{q}(\omega)  V^*_{\alpha q} G_{\alpha\beta}^a(\omega) ] \end{eqnarray}  Then  \begin{eqnarray}  Q^>(\omega) = \frac{ e^2}{\hbar^2}\sum_{k\beta,q\gamma,\alpha\delta\nu\mu} \int \frac{d\epsilon}{2\pi}\Biggr\{[V^*_{\beta k} g^{r,h}_{k}(\omega) V_{\alpha k} G_{\alpha\gamma}^>(\omega)+g^{>,h}_{k}(\omega) V_{\alpha k} G_{\alpha\gamma}^a(\omega)] [V^*_{\alpha q} g^{r}_{q}(\omega) V_{\beta q} G_{\alpha\beta}^r(\omega)+ V^*_{\alpha q} g^{<}_{q}(\omega) V_{\beta q} G_{\alpha\beta}^a(\omega) ]  \end{eqnarray}