Renormalization Effects of Leptonic Decay Coupling Constants in BrokenSU3Symmetry

By analyzing the tensor ${T_{\nu 3}}^{\mu 3}$ in $U_3$, the theorem of Ademollo and Gatto on the nonrenormalization of the vector leptonic decay coupling constants to first order in symmetry breaking is reproduced. To second order, by analyzing ${T_{\nu 33}}^{\mu 33}$, it is found that there exists one sum rule among the strangeness-changing vector coupling constants. For the axial vector coupling constants there are in general two sum rules to first order in symmetry breaking. In the $\varphi -\omega$ mixing model one obtains an additional sum rule. With regard to the equaltime commutation relations of weak currents in broken $S{U}_3$, a theorem is obtained that the one-particle approximation always leads to results which are consistent only with exact symmetry. A qualitative discussion of the relation between the two results is given.