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