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 $\phi$.