Schwarz Inequality for One-Photon Annihilation, Electroproduction, and the Two-Photon Process

It is demonstrated that the Schwarz inequality gives useful relations between the onephoton annihilation process $e^{+}+e^{-}\to \mathrm{any}\mathrm{hadrons}$, the electroproduction $e+A\to e+\mathrm{anything}$, and the two-photon process $e^{\pm }+e^{-}\to e^{\pm }+e^{-}+A$, where $A$ is an arbitrary hadronic state with positive charge conjugation. Particularly, the ${\pi }^0\gamma \gamma$ vertex function, if it decreases at all, is shown to decrease not slower than ${(-q^2)}^{-\frac{1}{2}}$ as one of the virtual-photon masses $q^2$ increases. Possible applications to various other processes are suggested.