  The chiral kinetic theory of Weyl fermions with collisions in the presence of
weak electric and magnetic fields is derived from quantum field theories. It is
found that the side-jump terms in the perturbative solution of Wigner functions
play a significant role for the derivation. Moreover, such terms manifest the
breaking of Lorentz symmetry for distribution functions. The Lorentz covariance
of Wigner functions thus leads to modified Lorentz transformation associated
with side-jump phenomena further influenced by background fields and
collisions.
