= Two-photon fermion Ward identity
The two <photon> orders in a tree-level charged-<fermion> amplitude must be summed. Contracting one <photon> vertex with its momentum writes the contracted slash as a difference of inverse <Dirac propagators>. The external <Dirac equations> remove the <on shell> inverse factors; the two remaining terms have equal size and opposite sign. Thus the sum vanishes under the momentum replacement although individual diagrams generally do not. This implements the gauge equivalence of <photon polarization vectors>.
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