Current Algebra and Vertex Functions

Abstract

A method is given for calculating vertex functions involving three currents obeying chiral SU(2)\ensuremath{\bigotimes} SU(2) commutation relations, without using soft-pion approximations. The procedure assumes one-particle dominance of intermediate states. The Weinberg sum rule emerges as a consequence of the vanishing of $q$-number Schwinger terms. The charge radius of the pion is obtained and is in agreement with existing data.