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Is the Dirac string continuous? Suppose I have a point magnetic charge. Do the necessary singularities of the vector potential lie on a continuous curve in 3D space?

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  • $\begingroup$ The vector potential (as a globally defined gauge field) is only singular at the point of the magnetic charge. It's a local coordinate representation of it that develops singularities along the Dirac string, but the actual vector potential does not (that's the reason why the string has to be unobservable - it's a coordinate artifact, not an actual object of the theory), see this answer of mine. $\endgroup$ – ACuriousMind Oct 11 '15 at 13:38

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