Chiral anomaly in Weyl systems: no violation of classical conservation laws

TL;DR

This paper clarifies that the chiral anomaly in Weyl systems does not violate classical conservation laws, as the anomalous term can be interpreted as a quantum current consistent with classical density balance.

Contribution

It demonstrates that the so-called chiral anomaly does not violate classical conservation laws, reinterpreting the anomalous term as a quantum current within classical density balance.

Findings

The anomalous term can be expressed as a quantum current.

Chiral anomaly does not violate classical conservation laws.

Reinterpretation of the anomaly as a quantum current.

Abstract

The anomalous term $\sim\mathbf{EB}$ in the balance of the chiral density can be rewritten as quantum current in the classical balance of density. Therefore it does not violate classical conservation laws as it is claimed to be caused by quantum fluctuations.