Chiral and axial anomalies in the framework of generalized Hamiltonian BFV-quantization

TL;DR

This paper develops a regularization scheme for gauge fields with chiral or axial fermions within Hamiltonian BFV-quantization, revealing how anomalies affect the algebra and BRST symmetry.

Contribution

It introduces a regularization approach that connects Schwinger terms with covariant anomalies and analyzes their impact on BRST nilpotency and conservation.

Findings

Schwinger terms are consistent with covariant divergence anomalies.

Regularized quantum master equations show breakdown of BRST nilpotency.

Wess-Zumino conditions contradict covariant Schwinger terms.

Abstract

The regularization scheme is proposed for the constrained Hamiltonian formulation of the gauge fields coupled to the chiral or axial fermions. The Schwinger terms in the regularized operator first-class constraint algebra are shown to be consistent with the covariant divergence anomaly of the corresponding current. Regularized quantum master equations are studied, and the Schwinger terms are found out to break down both nilpotency of the BRST-charge and its conservation law. Wess-Zumino consistency conditions are studied for the BRST anomaly and they are shown to contradict to the covariant Schwinger terms in the BRST algebra.