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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]
     
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  3. Dec 19, 2012 #2

    PeterDonis

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    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

    PeterDonis

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    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.
     
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