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We give a brief overview of the kinetic theory for spin-1/2 fermions inWigner function formulism. The chiral and spin kinetic equations can be derivedfrom equations for Wigner functions. A general Wigner function has 16components which satisfy 32 coupled equations. For massless fermions, thenumber of independent equations can be significantly reduced due to thedecoupling of left-handed and right-handed particles. It can be proved that outof many components of Wigner functions and their coupled equations, only onekinetic equation for the distribution function is independent. This is calledthe disentanglement theorem for Wigner functions of chiral fermions. Formassive fermions, it turns out that one particle distribution function andthree spin distribution functions are independent and satisfy four kineticequations. Various chiral and spin effects such as chiral magnetic and voticaleffects, the chiral seperation effect, spin polarization effects can beconsistently described in the formalism.

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