deletions | additions       diff --git a/Magnetic response.tex b/Magnetic response.tex  index d7fdddf..b67ec96 100644  --- a/Magnetic response.tex  +++ b/Magnetic response.tex 
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In general, the gauge-invariant non-local potential is given by  %  \begin{equation}  \label{gauge-methods} \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}'} \vec{\mathrm{A}}(\vec{x},t) \cdot d\vec{x}) \mathrm{d}\vec{x})  \ .  \end{equation}  The integration path can be any one that connects the two