Axial-Vector Vertex in Spinor Electrodynamics
1969/01/25 by Stephen L. Adler · 2 voices · 89 citations
Physics and Astronomy · #Atomic and Subatomic Physics Research #Black Holes and Theoretical Physics #Quantum Chromodynamics and Particle Interactions
paper · doi:10.1103/physrev.177.2426
openalex publication_date 1969/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Abstract
Working within the framework of perturbation theory, we show that the axial-vector vertex in spinor electrodynamics has anomalous properties which disagree with those found by the formal manipulation of field equations. Specifically, because of the presence of closed-loop "triangle diagrams," the divergence of axial-vector current is not the usual expression calculated from the field equations, and the axial-vector current does not satisfy the usual Ward identity. One consequence is that, even after the external-line wave-function renormalizations are made, the axial-vector vertex is still divergent in fourth- (and higher-) order perturbation theory. A corollary is that the radiative corrections to \ensuremathνll elastic scattering in the local current-current theory diverge in fourth (and higher) order. A second consequence is that, in massless electrodynamics, despite the fact that the theory is invariant under \ensuremathγ5 tranformations, the axial-vector current is not conserved. In an Appendix we demonstrate the uniqueness of the triangle diagrams, and discuss a possible connection between our results and the \ensuremathπ0\ensuremath→2\ensuremathγ and \ensuremathη\ensuremath→2\ensuremathγ decays. In particular, we argue that as a result of triangle diagrams, the equations expressing partial conservation of axial-vector current (PCAC) for the neutral members of the axial-vector-current octet must be modified in a well-defined manner, which completely alters the PCAC predictions for the \ensuremathπ0 and the \ensuremathη two-photon decays.
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