Axial-Vector Current in Spinor Electrodynamics

概要

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A formalism for the axial-vector current j_μ^5 defined in spinor electrodynamics is presented in order to preserve the formal divergence relation of j_μ^5. The only deviation from the conventional way of field theory is to introduce a simple kinematical pole in some matrix element of j_μ^5. The vertex parts of j_μ^5 are divided into two parts, one contributing to ∂^μj_μ^5 and necessarily satisfying gauge conditions, and the other giving a vanishing contribution to ∂^μj_μ^5. It is shown that renormalization of ultraviolet divergences can be carried out without any trouble in the former, while in the latter it is difficult to keep obvious gauge invariance. Adler's low-energy theorem, which has some relevance to π^0→2γ decay, manifests itself as a consequence of gauge invariance and the divergence relation of j_μ^5.
理論物理学刊行会の論文
1970-11-25