The Subtleties of the Wigner Function Formulation of the Chiral Magnetic Effect

TL;DR

This paper examines the limitations of the Wigner function approach to the chiral magnetic effect, identifying issues with current conservation and proposing regularization solutions to address ultraviolet divergences.

Contribution

It highlights the problems in the current Wigner function formulation for the chiral magnetic effect and suggests a regularization method to improve its consistency.

Findings

Identifies issues with current conservation in the Wigner function approach.

Proposes Pauli-Villars regularization to fix ultraviolet divergence problems.

Clarifies the applicability limits of the Wigner function in this context.

Abstract

We assess the applicability of the Wigner function formulation in its present form to the chiral Magnetic Effect and noted some issues regarding the conservation and the consistency of the electric current in the presence of an inhomogeneous and time dependent axial chemical potential. The problems are rooted in the ultraviolet divergence of the underlying field theory associated with the axial anomaly and can be fixed with the Pauli-Villars regularization of the Wigner function.