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, $R:{{{→}}{A}}_{{μ}}(x){→}{{{→}}{A}}_{{μ}}(x) + {{{→}}{r}}_{{μ}}$, 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 ${{Γ}}R^{{⋯}{μ}{⋯}}({},q,{})$ as $0 = {{Γ}}R^{{⋯}{μ}{⋯}}({},q=0,{})$.