Solving "If the Photon Had Mass m" Problem with Gauss' Law

[saleem]

hi

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

 

[hellfire]

Gauss law holds because \nabla E = 4 \pi \rho with E = - \nabla \phi. In case of electrostatics (no time dependence) this condition is the same than the wave equation of \phi in the Lorenz gauge. Now the point is that if the photon had mass \phi 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 \phi.