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Homework Help: Photon mass

  1. May 6, 2007 #1

    I have this question, I need your help:

    If the photon had mass "m" , show that the Gauss' law would no longer be true.
    Note that the electric poential for a point charge would then have a form
    V(r) = e/r exp ( -mc/h * r )

    Thank you
  2. jcsd
  3. May 8, 2007 #2


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    Science Advisor

    Gauss law holds because [itex]\nabla E = 4 \pi \rho[/itex] with [itex]E = - \nabla \phi[/itex]. In case of electrostatics (no time dependence) this condition is the same than the wave equation of [itex]\phi[/itex] in the Lorenz gauge. Now the point is that if the photon had mass [itex]\phi[/itex] would not longer satisfy a wave equation but a Klein-Gordon equation. For the second part of the exercise, rewrite the Klein-Gordon equation in spherical coordinates and integrate to find [itex]\phi[/itex].
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