= Charge selection rule for complex scalar correlators
{title2=$\langle\phi^r(\phi^*)^s\rangle=0\quad(r\ne s)$}
In a phase-invariant <vacuum>, a correlator with $r$ insertions of $\phi$ and $s$ of $\phi^*$ gains the phase $e^{i\alpha(r-s)}$. Its invariance for all real $\alpha$ forces it to vanish unless $r=s$. Balanced local interactions and the absence of same-charge free contractions give the same rule order by order in <Wick's theorem>. A symmetry-breaking vacuum is an essential exception to the vacuum-invariance premise.
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