  We develop a general formalism for the quantum kinetics of chiral fermions in
a background electromagnetic field based on a semiclassical expansion of
covariant Wigner functions in the Planck constant $\hbar$. We demonstrate to
any order of $\hbar$ that only the time-component of the Wigner function is
independent while other components are explicit derivative. We further
demonstrate to any order of $\hbar$ that a system of quantum kinetic equations
for multiple-components of Wigner functions can be reduced to one chiral
kinetic equation involving only the single-component distribution function.
These are remarkable properties of the quantum kinetics of chiral fermions and
will significantly simplify the description and simulation of chiral effects in
heavy ion collisions and Dirac/Weyl semimetals. We present the unintegrated
chiral kinetic equations in four-momenta up to $O(\hbar ^2)$ and the integrated
ones in three-momenta up to $O(\hbar)$. We find that some singular terms emerge
in the integration over the time component of the four-momentum, which result
in a new source term contributing to the chiral anomaly, in contrast to the
well-known scenario of the Berry phase term. Finally we rewrite our results in
any Lorentz frame with a reference four-velocity and show how the non-trivial
transformation of the distribution function in different frames emerges in a
natural way.
