deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 11178a9..45cc538 100644  --- a/untitled.tex  +++ b/untitled.tex 
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\begin{equation}  G_{kq}^{h,t}(\omega) = G_{kq}^{h,t}(\omega)\delta_{kq} + \sum_{\beta\gamma} g_{k}^{h,t}(\omega) V_{\gamma k} G^{t}_{\gamma\beta}(\omega)V_{\beta q}^* g_{q}^{h,t}(\omega)\,,  \end{equation} \begin{multline}  S^>(\omega)=\frac{e^2}{\hbar^2}\sum_{k\beta,q\gamma} \frac{1}{2\pi}\int_{-\infty}^\infty  d\omega \frac{1}{2\pi}\int_{-\infty}^\infty d\epsilon   \\   \Biggr\{  V_{\beta k} V_{\gamma q}^{*} [G^>_{\beta\gamma}(\epsilon) G^{h,<}_{qk}(\omega+\epsilon) - G^{>}_{\beta q}(\epsilon)G^{h,<}_{\gamma k}(\epsilon+\omega)]  + V_{\beta k}^{*}V_{\gamma q} [G^{>,t}_{kq}(\epsilon_1) G^{<}_{\gamma\beta}(\epsilon+\omega) - G^{h,>}_{k\gamma}(\epsilon)G^{<}_{q \beta}(\epsilon+\omega)]\Biggr\}\,,  \end{multline}