deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 540bdde..bde5fa3 100644  --- a/untitled.tex  +++ b/untitled.tex 
...
\end{eqnarray}  \begin{eqnarray}  Q^{>,4}(\omega) = \frac{ 4e^2}{\hbar^2}\sum_{k\beta,q\gamma,\alpha\mu\nu\tau } \int \frac{d\epsilon}{2\pi}[\Gamma_{\beta\alpha}]G_{\alpha\gamma}^a(\epsilon) [-i\Gamma_{\gamma\tau}]G_{\tau\mu}^r(\omega+\epsilon)\Gamma_{\mu\nu} G_{\nu\beta}^a(\omega+\epsilon)(f_h(\omega+\epsilon)+f_e(\omega+\epsilon))(1-f_h(\epsilon)) [-i\Gamma_{\gamma\tau}]G_{\tau\beta}^a(\omega+\epsilon)f_e(\omega+\epsilon)(1-f_e(\epsilon))  \end{eqnarray}  We can now express the total contribution for $Q^>$ and $Q^<$ as