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\begin{equation}
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\begin{equation}
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\Tilde{\bF}(s) = \bF + \bF^{(2)}(s)
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\Tilde{\bF}(s) = \bF + \bF^{(2)}(s)
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\qq{with}
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\qq{with}
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\Tilde{\bF}_{pq}(s) = \delta_{pq} \eps_{p} +
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\Tilde{\bF}_{pq}(s) = \delta_{pq} \eps_{p} - \sum_{rm} \frac{\Delta_m^{pr} \Delta_m^{qr}}
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\end{equation}
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\end{equation}
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\end{block}
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\end{block}
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\begin{block}{Regularized $GW$ self-energy}
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\begin{block}{Regularized $GW$ self-energy}
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