Solution
= Solution
An infinitesimal constant phase change has $\delta\phi=-iq\alpha\phi$ and $\delta\phi^*=iq\alpha\phi^*$. Both the <derivative> product and the <mass> term are invariant. <Noether's theorem> gives, per unit $\alpha$,
$$
j^\mu=(\partial^\mu\phi^*)(-iq\phi)
+(\partial^\mu\phi)(iq\phi^*)
=iq(\phi^*\partial^\mu\phi-\phi\partial^\mu\phi^*).
$$
Thus \b[the global phase symmetry supplies the conserved current in part a].