How do I find an equation analogous to \begin{equation} \mathcal{L}(q,\dot q)=\frac12 m \dot q ^2-q\phi+q\vec{\dot q}\cdot \vec A\quad\quad \text{where}\quad \vec B =\vec\nabla\times\vec A, \quad \vec E=-\vec\nabla\phi-\partial_t\vec A \end{equation} for magnetic monopole instead of the electric point charge coupling to the $A$-field?
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1$\begingroup$ Related: physics.stackexchange.com/q/343075/2451 , physics.stackexchange.com/q/59874/2451 , physics.stackexchange.com/q/261257/2451 , physics.stackexchange.com/q/164182/2451 and links therein. $\endgroup$– Qmechanic ♦Apr 3, 2021 at 13:45
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$\begingroup$ See the Seiberg-Witten equation on Wikipedia. $\endgroup$– Mozibur UllahApr 3, 2021 at 13:48
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