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

  1. Mar 8, 2013 #1
    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?
  2. jcsd
  3. Mar 8, 2013 #2
  4. Mar 8, 2013 #3
    Thank you. But there representing the equations of Maxwell, expressed in terms of the field, and not in terms of the potentials.
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