Axial vector current anomaly problem without regularization in Dyson scheme

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.