Axial-vector current and dimensional regularization

The properties of the axial-vector current are investigated using the dimensional-regularization scheme. The problem of defining an appropriate generalization of γ₅ in n dimensions is discussed, and previous work is briefly reviewed. For the VVA triangle, in QED, we find that the dimensional scheme provides for vector current conservation, with the divergence of the axial-vector current anomalous. This is shown unambiguously without specifying the anticommuting nature of γ₅ in n dimensions. If one arranges to have two species of fermions with different masses and equal but opposite couplings to the axial-vector current, the VVA anomaly is proportional to n-4, being fully canceled only at $n=4$. However, the behavior of the triangle amplitude for large external momenta is reduced by two powers, and the resulting softened triangle does not give rise to any finite (as n→4) anomalies when inserted in higher-order diagrams. Finally, the appropriate generalization of γ₅ for even-parity fermion loops is shown to be totally anticommuting, and the validity of Ward identities for two-point functions is demonstrated.