deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 3ac0c70..f212764 100644  --- a/untitled.tex  +++ b/untitled.tex 
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&M^>(\omega)=\frac{4 e^2}{\hbar^2}\sum_{k\beta,q\gamma,\alpha\delta\nu\mu} \int \frac{d\epsilon}{2\pi}\Biggr\{ \Gamma_{\beta\gamma} G^{r}_{\gamma\nu}(\omega+\epsilon)\Gamma_{\nu\mu}G^{a}_{\mu\beta}(\omega+\epsilon)](f_{e}(\omega+\epsilon)+f_h(\omega+\epsilon)) (1-f_{e}(\epsilon)] \\  & [-i\Gamma_{\beta\alpha}] G^{r}_{\alpha\delta}(\epsilon) \Gamma_{\delta\gamma} G^{r}_{\gamma\nu}(\omega+\epsilon)\Gamma_{\nu\mu}G^{a}_{\mu\beta}(\omega+\epsilon)](f_{e}(\omega+\epsilon)+f_h(\omega+\epsilon))(1-f_h(\epsilon)) +   \\   &[\sum_{\theta\tau} [-i\Gamma_{\beta\alpha}] G^{r}_{\alpha\theta}(\omega+\epsilon)\Gamma_{\theta\tau}G^{a}_{\tau\delta}(\omega+\epsilon) G^{r}_{\alpha\theta}(\omega+\epsilon)\Gamma_{\theta\tau}G^{a}_{\tau\delta}(\epsilon)  [i\Gamma_{\delta\gamma}] G^{r}_{\gamma\nu}(\omega+\epsilon)\Gamma_{\nu\mu}G ^{a}_{\mu\beta}(\omega+\epsilon)] \\  &(f_{e}(\omega+\epsilon)+f_h(\omega+\epsilon)) (1-f_{e}(\epsilon)+1-f_h(\epsilon)) +   [\Gamma_{\beta\alpha}(\omega+\epsilon) G^{a}_{\alpha\delta}(\omega+\epsilon) [\Gamma_{\beta\alpha}(\epsilon) G^{a}_{\alpha\delta}(\epsilon)  [i\Gamma_{\delta\gamma}] G^{r}_{\gamma\nu}(\omega+\epsilon)\Gamma_{\nu\mu}G ^{a}_{\mu\beta}(\omega+\epsilon)] \\  & (f_{e}(\omega+\epsilon)+f_h(\omega+\epsilon)(1-f_h(\epsilon))) \Biggr\}  \end{align*}