= Scattering charge selection rule from global gauge symmetry
{title2=$[Q,S]=0\ \Longrightarrow\ (Q_f-Q_i)\langle f|S|i\rangle=0$}
For a conserved charge $Q$ and invariant vacuum, its global symmetry commutes with the <S-matrix>. Matrix elements between charge eigenstates give the displayed selection rule. Constant electromagnetic phases cancel at every QED vertex, and nonzero physical amplitudes conserve total charge. Local <gauge invariance> strengthens this global rule to the <Ward-Takahashi identity>.
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