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Rosa edited untitled.tex
about 8 years ago
Commit id: 266baa955aa175e5abb0debb44aeece6f14479ce
deletions | additions
diff --git a/untitled.tex b/untitled.tex
index cf5ef39..92ceea9 100644
--- a/untitled.tex
+++ b/untitled.tex
...
G^>_{\beta q}(\omega+\epsilon) = \sum_\gamma [G_{\beta\gamma}^r(\omega+\epsilon) V_{\gamma q} g^{>}_{q}(\omega+\epsilon)+ G_{\beta\gamma}^>(\omega+\epsilon) V_{\gamma q} g^{a}_{q}(\omega+\epsilon)]
\end{eqnarray}
\begin{eqnarray}
G^{<,h}_{\gamma k}(\omega) = \sum_\beta [G_{\gamma\beta}^r(\omega)
V_{\beta V^*_{\beta k} g^{<,h}_{k}(\omega)+ G_{\gamma\beta}^<(\omega)
V_{\beta V^*_{\beta k} g^{a,h}_{k}(\omega)]
\end{eqnarray}
Then, we have
\begin{eqnarray}
&&N(\omega)=(e^2/h)\sum_{k\beta,q\gamma, \nu\mu} \int \frac{d\epsilon}{2\pi} V_{\beta k} V^*_{\gamma q}
[G_{\beta\nu}^r(\omega+\epsilon) V_{\nu q} g^{>}_{q}(\omega+\epsilon)+ G_{\beta\nu}^>(\omega+\epsilon) V_{\nu q} g^{a}_{q}(\omega+\epsilon)]
\\ \nonumber
&&[G_{\gamma\mu}^r(\omega)
V_{\mu V^*_{\mu k} g^{<,h}_{k}(\omega)+ G_{\gamma\mu}^<(\omega)
V_{\mu V^*_{\mu k} g^{a,h}_{k}(\omega)]
\end{eqnarray}