Renormalization of the Axial-Vector Vertex in Spinor Electrodynamics

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Abstract
In the usual method of regularization, the regulator axial-vector current is not conserved. Consequently, the regularized axial-vector current does not, in general, satisfy the ordinary divergence equation derived by using field equations. The anomalous axial-vector divergence equation of spinor electrodynamics is shown to be related to this difficulty of regularization. Using the chiral-invariant regularization and the generalized renormalization procedure developed previously, we show how to obtain an axial-vector vertex which obeys the normal Ward-Takahashi identity and is renormalizable to all orders of perturbation theory. Our general argument is illustrated by an explicit calculation of the fourth-order contribution to the axial-vector vertex from the anomalous triangle loop diagram. We also observe that the renormalized axial-vector vertex, which is well behaved from the point of view of perturbation theory, violates the requirement of generalized unitarity.

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