# An Empty Chiral Rotation for the Adler-Bell-Jackiw Anomaly

## TL;DR

This paper challenges the traditional view that the Adler-Bell-Jackiw anomaly arises from chiral rotation non-invariance, proposing instead that the associated Jacobian is indeterminate and carries no physical information.

## Contribution

It offers a novel explanation that the ABJ anomaly is not due to a nontrivial Jacobian, contradicting the conventional understanding.

## Key findings

- The fermionic measure definition reproduces Feynman diagrams.
- The Jacobian factor in chiral transformations is indeterminate.
- The ABJ anomaly is explained as a non-physical artifact.

## Abstract

This is an article which intends to shake down the traditional belief that the celebrated Adler-Bell-Jackiw anomaly stems from the chiral rotation non-invariance of the fermionic measure. The fermionic functional integration measure in quantum field theory should be defined so as to reproduce the standard Feynman diagrammatic expansion. This implies that a plain definition of the fermionic measure automatically serves such a purpose. A dilemma then arises: how could one identify the ABJ anomaly as a nontrivial Jacobian factor for a chiral transformation ? The true answer is indeed surprising and unexpected, that is, the Jacobian factor is actually a random and indeterminate object, hence it carries no physical information. A true explanation for the ABJ anomaly is suggested.