
\item Homework, due F 12/1/2017 before class. Retarded potential 
and Lorenz gauge: Show that current conservation $\partial_{\mu} 
J^{\mu}(\{x^v\})=0$ implies that the retarded solution for the 
potential [Eq.~(7.50) of the book]
$$ \Phi^{\mu}(\{x^{\nu}\}) = \frac{1}{c} \int d^3y\,\frac{J^{\mu}
   (x^0-|\vec{x}-\vec{y}|,\vec{y})}{|\vec{x}-\vec{y}|} $$
fulfills the Lorenz gauge $\partial_{\mu}\Phi^{\mu} (\{x^{\nu}\})=0$.
\bigskip 

