We give a brief overview of the kinetic theory for spin-1/2 fermions in Wigner function formalism. 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 vortical effects, the chiral separation effect, spin polarization effects can be consistently described in the formalism.

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Wigner 函数形式中自旋 1/2 费米子的量子动力学理论

我们简要概述了 Wigner 函数形式中自旋 1/2 费米子的动力学理论。手性和自旋动力学方程可以从 Wigner 函数方程导出。一般的 Wigner 函数有 16 个分量，它们满足 32 个耦合方程。对于无质量费米子，由于左手和右手粒子的解耦，独立方程的数量可以显着减少。可以证明，在 Wigner 函数的许多分量及其耦合方程中，只有一个分布函数的动力学方程是独立的。这被称为手性费米子的 Wigner 函数的解缠结定理。对于大质量费米子，1个粒子分布函数和3个自旋分布函数相互独立，满足4个动力学方程。