We show that the leading divergences in weak nonleptonic decays can be expressed in terms of time-ordered products of $\sigma$ commutators (to all orders in the semiweak coupling constant). We formulate nontrivial criteria for the $\sigma$ commutators from which the leading divergencies in strangeness-changing nonleptonic interactions can be shown to vanish in any order. The remaining divergences are then of the same type as those in the radiative corrections.

• Received 26 November 1968

DOI:https://doi.org/10.1103/PhysRev.179.1417