Current Algebra and Ward Identities: Three- and Four-Point Functions

We present a technique which allows us to display explicitly all the information which current algebra yields about $n$-point functions of vector and axial-vector currents. We write all three- and four-point functions in terms of a few primitive functions which are not determined by current algebra. Any approximation to these functions (subject to a single constraint) when used in our formulation yields three- and four-point functions guaranteed to satisfy all constraints imposed by current algebra and partially conserved axial-vector current. We give a very simple model where the primitive functions are given by as smooth functions of the momenta as possible and apply this model to the ${\pi }^{+}-{\pi }^0$ electromagnetic mass difference, $A_1$ decay, and $\pi -\pi$ and $\pi -\rho$ scattering.