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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Qmechanic
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1Related: https://physics.stackexchange.com/q/343075/2451 , https://physics.stackexchange.com/q/59874/2451 , https://physics.stackexchange.com/q/261257/2451 , https://physics.stackexchange.com/q/164182/2451 and links therein. – Qmechanic Apr 03 '21 at 13:45
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See the Seiberg-Witten equation on Wikipedia. – Mozibur Ullah Apr 03 '21 at 13:48