Renormalization of Chirally Invariant Lagrangians

We discuss the renormalization problem for chirally invariant Lagrangians constructed from the pion isovector fields alone. We find that $S$-matrix elements have ultraviolet divergences even after the damping from resummation has been effected. The counterterms necessary to remove such divergences are shown to modify the original current commutation relations; it is not possible that these divergences cancel amongst themselves. We conclude that the current commutation relations are inconsistent with the Lagrangian formulation, unless they are changed or further particles are introduced.