deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 7783465..adc8026 100644  --- a/untitled.tex  +++ b/untitled.tex 
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S^{>,3}(\omega)= \frac{-4 e^2}{\hbar^2} \int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{\beta\gamma\alpha\delta} G^r_{\beta \alpha}(\epsilon) \Gamma_{\alpha\delta} G^a_{\delta \gamma}(\epsilon) [-i\Gamma_{\gamma\gamma}] G^{r}_{\gamma\beta}(\omega+\epsilon) G^{a}_{\gamma\beta}(\omega+\epsilon) [i\Gamma_{\beta\beta}][(1-f_{e}(\epsilon))+(1-f_{h}(\epsilon))] [f_{e}(\epsilon+\omega)+f_{h}(\epsilon+\omega)]   \end{eqnarray}  \begin{eqnarray}  S^{>,4}(\omega) = \frac{e^2}{\hbar^2} \frac{-4e^2}{\hbar^2}  \int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{\beta\gamma\alpha\delta} G^r_{\beta \alpha}(\epsilon) \Gamma{\alpha\delta} \Gamma_{\alpha\delta}  G^a_{\delta \gamma}(\epsilon) \Gamma_{\gamma\gamma} G^{a}_{\gamma\beta}(\omega+\epsilon) [i\Gamma_{0,\beta\beta}][(1-f_{e}(\epsilon))+(1-f_{h}(\epsilon))] [i\Gamma_{\beta\beta}][(1-f_{e}(\epsilon))+(1-f_{h}(\epsilon))]  f_{h}(\epsilon+\omega) \end{eqnarray}