A consistent description of kinetic equation with triangle anomaly

TL;DR

This paper develops a consistent kinetic equation framework incorporating triangle anomalies, ensuring compatibility with thermodynamic entropy principles and conservation laws, and determines correction terms for distribution functions.

Contribution

It introduces a method to incorporate triangle anomalies into kinetic equations while satisfying entropy and conservation constraints, providing explicit correction terms.

Findings

Derived constraining equations from the entropy principle.

Determined correction terms for distribution functions in one and two charge cases.

Ensured compatibility of anomaly-induced terms with conservation laws.

Abstract

We provide a consistent description of the kinetic equation with triangle anomaly which is compatible with the entropy principle of the second law of thermodynamics and the charge/energy-momentum conservation equations. In general an anomalous source term is necessary to ensure that the equations for the charge and energy-momentum conservation are satisfied and that the correction terms of distribution functions are compatible to these equations. The constraining equations from the entropy principle are derived for the anomaly-induced leading order corrections to the particle distribution functions. The correction terms can be determined for minimum number of unknown coefficients in one charge and two charge cases by solving the constraining equations.