Infrared behavior in non-Abelian gauge theories

The knowledge of the renormalization constants in ultraviolet-free non-Abelian gauge theories is exploited in exposing a new symmetry, $R:{\overrightarrow{A}}_{\mu }\mathrm{}\left(x\right)\mathrm{}\to {\overrightarrow{A}}_{\mu }\mathrm{}\left(x\right)\mathrm{} + {\overrightarrow{r}}_{\mu }$, under which the renormalized field equations of such theories are invariant. As a consequence, we derive the low-energy theorem for the renormalized proper vertices ${\Gamma }_R^{\cdots \mu \cdots }(\dots ,q,\dots )$ as $0 = {\Gamma }_R^{\cdots \mu \cdots }(\dots ,q=0,\dots )$.