deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 4fdd6cf..41ae010 100644  --- a/untitled.tex  +++ b/untitled.tex 
...
\end{eqnarray}  We replace now  \begin{align*}  &G_{kq}^{h,>}(\epsilon) = g_{q}^{h,>}(\epsilon)+  \sum_{\alpha\delta} [g_{k}^{h,r}(\epsilon) V_{\alpha k} G^{r}_{\alpha\delta}(\epsilon)V_{\delta q}^* g_{q}^{h,>}(\epsilon) +g_{k}^{h,r}(\epsilon) V_{\alpha k} G^{>}_{\alpha\delta}(\epsilon)V_{\delta q}^* g_{q}^{h,a}(\epsilon)] \\  \nonumber  &+g_{k}^{h,>}(\epsilon) V_{\gamma k} G^{a}_{\gamma\beta}(\epsilon)V_{\beta q}^* g_{q}^{h,a}(\epsilon) ]\,,  \end{align*}  Then we get  \begin{align*}  &M^>(\omega)=\frac{2 i e^2}{\hbar^2}\sum_{k\beta,q\gamma,\nu\mu} \int \frac{d\epsilon}{2\pi}\  V_{\beta k}^{*} g_{q}^{h,>}(\epsilon) V_{\alpha k}   &\frac{2 i  e^2}{\hbar^2}\sum_{k\beta,q\gamma,\alpha\delta,\nu\mu} \int \frac{d\epsilon}{2\pi}\Biggr\{ V_{\beta k}^{*} g_{q}^{h,>}(\epsilon) V_{\alpha k} G^{r}_{\gamma\nu}(\omega+\epsilon) \Gamma_{\nu\mu} G^{a}_{\mu\beta}(\omega+\epsilon)(f_e(\omega+\epsilon)+f_h(\omega+\epsilon))  \\  & V_{\beta k}^{*} g_{k}^{h,r}(\epsilon) V_{\alpha k} G^{r}_{\alpha\delta}(\epsilon) V_{\delta q}^* g_{q}^{h,>}(\epsilon) V_{\gamma q} G^{r}_{\gamma\nu}(\omega+\epsilon) \Gamma_{\nu\mu} G^{a}_{\mu\beta}(\omega+\epsilon)(f_e(\omega+\epsilon)+f_h(\omega+\epsilon))  \\