Quantum kinetic theory for spin-1/2 fermions in Wigner function formalism

TL;DR

This paper reviews the kinetic theory for spin-1/2 fermions using Wigner functions, highlighting the reduction of complex equations to a few independent kinetic equations, and discusses various chiral and spin effects.

Contribution

It introduces the disentanglement theorem for Wigner functions of chiral fermions, simplifying the kinetic equations for massless and massive fermions.

Findings

Reduction of Wigner function components to a single kinetic equation for massless fermions.

Identification of independent distribution functions for massive fermions.

Consistent description of chiral magnetic, vortical, and spin polarization effects.

Abstract

We give a brief overview of the kinetic theory for spin-1/2 fermions in Wigner function formulism. The chiral and spin kinetic equations can be derived from equations for Wigner functions. A general Wigner function has 16 components which satisfy 32 coupled equations. For massless fermions, the number of independent equations can be significantly reduced due to the decoupling of left-handed and right-handed particles. It can be proved that out of many components of Wigner functions and their coupled equations, only one kinetic equation for the distribution function is independent. This is called the disentanglement theorem for Wigner functions of chiral fermions. For massive fermions, it turns out that one particle distribution function and three spin distribution functions are independent and satisfy four kinetic equations. Various chiral and spin effects such as chiral magnetic and votical effects, the chiral seperation effect, spin polarization effects can be consistently described in the formalism.