The fate of the vector potential in the case of the existence of a mag

[sergiokapone]

The vector potential in classical electrodynamics can be introduced due to the fact that the magnetic field is the vortex:
div \vec B = 0 → \vec B = rot \vec A
In the four-dimensional form (including gauge) Maxwell's equations look particularly beautiful:
\partial_{\mu}\partial^{\mu} A^{\nu} = j ^{\nu}
where A^{\nu} - 4-potential.

Given the existence of a monopole, the magnetic field is no longer a vortex. Then, how to change the form of Maxwell's equations in 4-dimensional form (via potentials)? Whether to reject the concept of the vector potential?

 

[Wiemster]

http://en.wikipedia.org/wiki/Magnetic_monopole

 

[sergiokapone]

http://en.wikipedia.org/wiki/Magnetic_monopole

Thank you. But there representing the equations of Maxwell, expressed in terms of the field, and not in terms of the potentials.