Dirac sea and chiral anomaly in the quantum kinetic theory

TL;DR

This paper reveals that the chiral anomaly in quantum kinetic theory originates from the Dirac sea or vacuum contribution, which affects the chiral kinetic equation for antiparticles, providing new insights into anomaly physics.

Contribution

It clarifies the origin of the chiral anomaly in the Wigner function formalism and shows how vacuum contributions modify the kinetic equations for antiparticles.

Findings

Chiral anomaly arises from the Dirac sea in the Wigner function formalism.

Vacuum contributions modify the chiral kinetic equation for antiparticles.

Revisiting the anomaly provides deeper understanding of quantum kinetic theory.

Abstract

We revisit the chiral anomaly in the quantum kinetic theory in the Wigner function formalism under the background field approximation. Our results show that the chiral anomaly is actually from the Dirac sea or the vacuum contribution in the un-normal-ordered Wigner function. We also demonstrate that this contribution modifies the chiral kinetic equation for antiparticles.