Quantum kinetic equation for fermionic fluids and chiral kinetic theory

We first review how one can establish the quantum kinetic equation for fluids of spin-1/2 particles. Then we present the construction of the semiclassical relativistic chiral kinetic equation of the fluid in the presence of the external electromagnetic fields. We derive the resulting nonrelativistic chiral kinetic theory. We calculated the particle number current density and showed that chiral effects are correctly generated. Moreover, it satisfies the anomalous continuity equation.