deletions | additions       diff --git a/Magnetic response.tex b/Magnetic response.tex  index b67ec96..01f767b 100644  --- a/Magnetic response.tex  +++ b/Magnetic response.tex 
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\begin{equation}  \label{eq:gauge-methods}  \langle \vec{r} | \hat{v}^{\vec{\mathrm{A}}}_{\text{nl}} | \vec{r}' \rangle =  \langle \vec{r} | \hat{v}_{\text{nl}}| \vec{r}' \rangle \mathrm{exp}(\frac{i}{c}\int_{\vec{r}}^{\vec{r}'} \mathrm{exp}\left(\frac{i}{c}\int_{\vec{r}}^{\vec{r}'}  \vec{\mathrm{A}}(\vec{x},t) \cdot \mathrm{d}\vec{x}) \mathrm{d}\vec{x}\right)  \ .  \end{equation}  The integration path can be any one that connects the two