  The covariant chiral kinetic equation (CCKE) is derived from the
4-dimensional Wigner function by an improved perturbative method under the
static equilibrium conditions. The chiral kinetic equation in 3-dimensions can
be obtained by intergation over the time component of the 4-momentum. There is
freedom to add more terms to the CCKE allowed by conservation laws. In the
derivation of the 3-dimensional equation, there is also freedom to choose
coefficients of some terms in $dx_{0}/d\tau$ and $d\mathbf{x}/d\tau$ ($\tau$ is
a parameter along the worldline, and $(x_{0},\mathbf{x})$ denotes the
time-space position of a particle) whose 3-mometum integrals are vanishing. So
the 3-dimensional chiral kinetic equation derived from the CCKE is not uniquely
determined in the current approach. To go beyond the current approach, one
needs a new way of building up the 3-dimensional chiral kinetic equation from
the CCKE or directly from covariant Wigner equations.
