Anomalies in Ward Identities for Three-Point Functions

We study the Ward identities for three-point functions of vector, axial-vector, scalar, and pseudoscalar densities constructed in a free-quark model. Divergences in the integral representations for the two- and three-point functions have the effect that not all of the formal Ward identities are satisfied in the model. After making full use of the ambiguities inherent in the definition of linearly divergent objects, as well as adding known polynomials to certain of the three-point functions, we find that only the Ward identities for three axial-vector densities and for one axial-vector and two vector densities remain unsatisfied. Arguments are presented that for $n$-point functions with $n>\mathrm{}3\mathrm{}$, the Ward identities are satisfied.