Massless Limit of Transport Theory for Massive Fermions

We studied the $m=0$ limit of different components of Wigner functions for massive fermions. Comparing with the chiral kinetic theory, we separated the vanishing part and non-vanishing part for vector and axial vector components, up to the first order of $\hbar$. Then we discussed the possible physical meaning of the vanishing and non-vanishing parts, and their different behavior at thermal equilibrium.