# Relativistic Quantum Kinetic Theory for Massive Fermions and Spin Effects

## TL;DR

This paper develops a comprehensive relativistic quantum kinetic theory for massive fermions with spin, deriving transport equations and demonstrating spin effects like the chiral separation effect, anomaly, and polarization in various physical systems.

## Contribution

It provides a complete first-order relativistic quantum kinetic framework for massive fermions, explicitly reducing Wigner equations to independent transport equations and illustrating spin effects.

## Key findings

- Derived explicit transport equations for massive fermions with spin.
- Calculated the chiral separation effect with mass correction.
- Showed how spin vorticity induces global polarization.

## Abstract

We present the complete first order relativistic quantum kinetic theory with spin for massive fermions derived from the Wigner function formalism in a concise form that shows explicitly how the 32 Wigner equations reduce to 4 independent transport equations. We solve modified on-shell conditions to obtain the general solution and present the corresponding transport equations in three different forms that are suitable for different purposes. We demonstrate how different spin effects arise from the kinetic theory by calculating the chiral separation effect with mass correction, the chiral anomaly from the axial current and the quantum magnetic moment density induced by vorticity and magnetic field. We also show how to generate the global polarization effect due to spin vorticity coupling. The formalism presented may serve as a practical theoretical framework to study different spin effects in relativistic fermion systems encountered in different areas such as heavy ion, astro-particle and condensed matter physics as well.