... | ... | @@ -45,6 +45,7 @@ R_{i\ell}\^\sigma(r;E_\text{F})$. |
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### Kohn-Sham susceptibility
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The transverse magnetic Kohn-Sham susceptibility is given by
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```math
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\chi^{\sigma\bar{\sigma}}_{0,ij}(\vec{r}\,,\vec{r}\,';\omega)
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&=& -\frac{1}{\pi}\!\int^{E_\text{F}}\!\!\!\!\text{d}E \nonumber \\
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... | ... | @@ -63,6 +64,7 @@ $\chi\^{-+}$, respectively. |
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Let us turn our attention to the Dyson equation for the GF, including
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the self-energy describing the coupling to the magnetic excitations:
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```math
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G_{ij}^\sigma(\vec{r}\,,\vec{r}\,';E)
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&=& G_{0,ij}^\sigma(\vec{r}\,,\vec{r}\,';E) + \sum_{pq}\!\int\!\!\text{d}\vec{r}_1\!\int\!\!\text{d}\vec{r}_2\; \times \nonumber\
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... | ... | |