Axial vector current anomaly problem without regularization in Dyson scheme

TL;DR

This paper demonstrates a regularization-free method within Dyson's scheme to calculate the axial vector current anomaly in four-dimensional Minkowski space, ensuring gauge invariance and unambiguous results.

Contribution

It applies Dyson's original scheme to the axial vector current anomaly, avoiding regularization and resolving divergence issues in a straightforward four-dimensional calculation.

Findings

Linearly divergent terms are canceled without ambiguity.

Gauge invariant results are obtained through symmetric tensor integration.

The method confirms the anomaly calculation without regularization.

Abstract

The loop momenta of a single Feynman diagram in momentum space can be assigned unambiguously within the 'Dyson scheme' without referring to the other Feynman diagrams in the complete set to some order of coupling constant for the certain process. This fact and the scheme which were provided in Dyson's original paper are applied to a typical relevant problem, i.e., the triangle diagrams of the 'axial vector current anomaly'. The calculation is done in four-dimension Minkowski space-time straightforwardly without the aid of any regularization. The linearly divergent terms are canceled sans incertitude. The logarithmically divergent symmetric integration (tensor integration) is investigated for obtaining the consistent and gauge invariant result.