Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to prove that Maxwell eqs. are covariant

  1. Dec 19, 2012 #1
    Is it enough to see the covariance of the wave equation the fourth-vector potential ([itex]\phi[/itex], [itex]\bar{A}[/itex]) satisfy? I mean, is this enough to prove the covariance of Maxwell equations?

    The equation would be [itex]∂_{\mu}[/itex][itex]∂^{\mu}[/itex][itex]A^{\nu} [/itex]=[itex]\frac{4\pi}{c}[/itex] [itex]J^{\nu}[/itex]

    [itex] [/itex]
  2. jcsd
  3. Dec 19, 2012 #2


    Staff: Mentor

    Why can't you just look at Maxwell's equations directly to see that they are covariant?

    [tex]\partial_{\mu} F^{\nu \rho} + \partial_{\nu} F^{\rho \mu} + \partial^{\rho} F^{\mu \nu} = 0[/tex]

    [tex]\nabla_{\mu} F^{\mu \nu} = 4 \pi J^{\nu}[/tex]
  4. Dec 19, 2012 #3
    Simply because is easier to look (using fourth-vectors) at the equations for the potentials instead of the equation for the fields.
  5. Dec 19, 2012 #4


    Staff: Mentor

    If the two equations are logically equivalent, yes, you could look at either one. But I don't think the wave equation for the 4-potential is logically equivalent to Maxwell's Equations; Maxwell's Equations imply the wave equation, but I'm not sure the converse is true.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook