Furry's theorem

Furry's theorem states that photon-only vacuum correlation functions with an odd number of insertions vanish in charge conjugation-invariant quantum electrodynamics. Each electromagnetic current or photon field is odd under charge conjugation, so an invariant vacuum makes the correlation function equal to minus itself.

Diagrammatically, reversing a charged-fermion loop cancels its partner when it has an odd number of photon attachments, with the relevant complete set of contributions included. The restriction concerns the specified insertions and symmetries. It is too broad to forbid every process with an odd number of photons merely because no charged external particle appears: another neutral source can itself carry odd charge-conjugation quantum number. Charged external states also require a separate transformation analysis.