deletions | additions       diff --git a/Magnetic response.tex b/Magnetic response.tex  index 6f6c0e9..0240535 100644  --- a/Magnetic response.tex  +++ b/Magnetic response.tex 
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%  \begin{equation}  \label{eq:iclmag1}  \delta \hat{\vec{v}}^{\mathrm{ICL}} = \delta \hat{\vec{v}}^{\mathrm{mag}} \vec{\hat{v}}^{\mathrm{mag}}  - \frac{i}{2c}\vec{\hat{r}}\times\left[\hat{\vec{r}}, v_{\text{nl}}\right]\ , \end{equation}  %  and a similar term for the second order perturbation. Using a different integration path, Pickard and Mauri~\cite{Pickard_2003} proposed the GIPAW method, that has the form