deletions | additions       diff --git a/untitled.tex b/untitled.tex  index a9ecd87..57390b8 100644  --- a/untitled.tex  +++ b/untitled.tex 
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S^{>,1}(\omega)= \frac{e^2}{\hbar^2}\int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{k,q,p\beta\gamma\alpha\delta} G^r_{\beta \alpha}(\epsilon) [V^*_{\alpha p} g^<_{p}(\epsilon)V_{ \delta p} + V_{\alpha p} g^{h,<}_{p}(\epsilon) V^*_{\delta p}]G^a_{\delta \gamma}(\epsilon)[V_{\beta k} g_{q}^{h,<}(\omega+\epsilon)V^*_{\gamma q}\delta_{kq}  \end{eqnarray}  \begin{eqnarray}  S^{>,2}(\omega)= S^{>,2}(\omega) =  \frac{e^2}{\hbar^2} \int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{k,q,p\beta\gamma\alpha\delta} G^r_{\beta \alpha}(\epsilon) [V_{\alpha p}^* g^<_{p}(\epsilon)V_{\delta p} + V_{\alpha p} g^{h,<}_{p}(\epsilon) V_{\delta p}^*]G^a_{\delta \gamma}(\epsilon) [V_{\gamma q}^* g_{q}^{h,r}(\omega+\epsilon) V_{\gamma q} G^{<}_{\gamma\beta}(\omega+\epsilon) V_{\beta k} g_{k}^{h,a}(\omega+\epsilon)V^_{\beta k}] g_{k}^{h,a}(\omega+\epsilon) V_{\beta k}^*]  \end{eqnarray}  \begin{eqnarray}  S^{>,3}(\omega)= \frac{e^2}{\hbar^2} \int_{-\infty}^\infty \sum_{k,q,p\beta\gamma\alpha\delta} G^r_{\beta \alpha}(\epsilon) [V^*_{\alpha p} g^<_{p}(\epsilon)V_{ \delta p} + V_{\alpha p} g^{h,<}_{p}(\epsilon) V^*_{\delta p}]G^a_{\delta \gamma}(\epsilon) [V_{\gamma q}^* g_{k}^{h,r}(\omega+\epsilon) V^*_{\gamma q} G^{<}_{\gamma\beta}(\omega+\epsilon)V_{\gamma q} g_{q}^{h,a}(\omega+\epsilon) V^*_{\gamma q}]