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A constant phase leaves the photon unchanged and makes every QED interaction vertex invariant: its one $\psi$ and one $\bar{\psi }$ acquire opposite phases. Thus the propagators and vertex factors in the QED Feynman rules are unchanged. A Green function with $n$ insertions of $\psi$ and $\bar{n}$ of $\bar{\psi }$ acquires the phase $e^{ie\chi (n-\bar{n})}$. For an invariant vacuum it can be nonzero only when its total inserted charge is zero.

Equivalently, the conserved charge operator $Q$ commutes with the S-matrix. If initial and final states have charges $Q_i,Q_f$, thenThe scattering charge selection rule from global gauge symmetry is thereforeIn diagrams the oriented fermion lines preserve charge at every vertex, and a photon is neutral. Pair creation is allowed because a particle and its antiparticle have opposite charges. Global phase invariance supplies this selection rule; local gauge invariance supplies the stronger momentum-dependent Ward-Takahashi identity.