deletions | additions       diff --git a/untitled.tex b/untitled.tex  index b3696f7..d1576f9 100644  --- a/untitled.tex  +++ b/untitled.tex 
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&[(1-f_{e}(\epsilon))f_{h}(\epsilon+\omega)+(1-f_{h}(\epsilon)) f_{h}(\epsilon+\omega)]  \end{align*}  \begin{align*}  &  P^{>,2}(\omega) = \frac{4e^2}{\hbar^2} \int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{\beta\gamma\alpha\delta\tau\theta}G^r_{\beta \alpha}(\epsilon) \Gamma_{\alpha\delta}(\epsilon) G^a_{\delta \gamma}(\epsilon) [-i\Gamma_{\gamma\tau}] G^{r}_{\tau\theta}(\omega+\epsilon) \Gamma_{\theta\beta}  &[(1-f_{e}(\epsilon))f_{h}(\epsilon+\omega)+(1-f_{h}(\epsilon)) \Gamma_{\theta\beta}[((1-f_{e}(\epsilon)+(1-f_{h}(\epsilon))  f_{h}(\epsilon+\omega)] \end{align*}  \begin{eqnarray}  & P^{>,3}(\omega)= \frac{-2i e^2}{\hbar^2} \int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{\beta\gamma\alpha\delta\tau\theta} G^r_{\beta \alpha}(\epsilon) \Gamma_{\alpha\delta} G^a_{\delta \gamma}(\epsilon) [-i\Gamma_{\gamma\tau}] G^{<}_{\tau\theta}(\omega+\epsilon) [i\Gamma_{\theta\beta}][(1-f_{e}(\epsilon))+(1-f_{h}(\epsilon))]