deletions | additions       diff --git a/untitled.tex b/untitled.tex  index b8151ed..1eea2e1 100644  --- a/untitled.tex  +++ b/untitled.tex 
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Let us treat first the following term: $\sum_{k\beta,q\gamma} V_{\beta k} V_{\gamma q}^{*} [G^>_{\beta\gamma}(\epsilon) G^{h,<}_{qk}(\omega+\epsilon) - G^{>}_{\beta q}(\epsilon)G^{h,<}_{\gamma k}(\epsilon+\omega)]$  Then,  \begin{eqnarray}  &&G_{kq}^{h,<}(\omega+\epsilon) = g_{q}^{h,<}(\omega+\epsilon)\delta_{kq} + \sum_{\beta\gamma} [g_{k}^{h,r}(\omega+\epsilon) V_{\gamma k} G^{r}_{\gamma\beta}(\omega+\epsilon)V_{\beta q}^* g_{q}^{<,t}(\omega)\nonumber g_{q}^{h,<}(\omega)\nonumber  \\  &&+g_{k}^{h,r}(\omega+\epsilon) V_{\gamma k} G^{<}_{\gamma\beta}(\omega+\epsilon)V_{\beta q}^* g_{q}^{a,t}(\omega+\epsilon)+g_{k}^{h,a}(\omega+\epsilon) g_{q}^{h,a}(\omega+\epsilon)+g_{k}^{h,a}(\omega+\epsilon)  V_{\gamma k} G^{a}_{\gamma\beta}(\omega+\epsilon)V_{\beta q}^* g_{q}^{<,t}(\omega+\epsilon)\,, g_{q}^{<,a}(\omega+\epsilon)\,,  \end{eqnarray}