Lorentz-violating extension of Wigner function formalism and chiral kinetic theory

TL;DR

This paper develops a Lorentz-violating extension of the Wigner function formalism and chiral kinetic theory, analyzing quantum kinetic equations, chiral currents, and anomalies in a Lorentz-violating background.

Contribution

It introduces a novel Lorentz-violating framework for quantum kinetic equations and chiral transport theory, extending existing models to include CPT and Lorentz symmetry-breaking effects.

Findings

Derived gauge-invariant Wigner function equations with Lorentz violation.

Calculated chiral currents and demonstrated anomalous effects.

Established a Lorentz-violating extended chiral transport equation.

Abstract

The quantum kinetic equation for the gauge-invariant Wigner function, constructed from spinor fields that obey the Dirac equation modified by CPT and Lorentz symmetry-violating terms, is presented. The equations for the components of the Wigner function in the Clifford algebra basis are accomplished. Focusing on the massless case, an extended semiclassical chiral kinetic theory in the presence of external electromagnetic fields is developed. We calculate the chiral currents and establish the anomalous magnetic and separation effects in a Lorentz-violating background. The chiral anomaly within the context of extended quantum electrodynamics is elucidated. Finally, we derive the semiclassical Lorentz-violating extended chiral transport equation.