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

1. Mar 8, 2013

### 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?

2. Mar 8, 2013

3. Mar 8, 2013

### sergiokapone

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