  From quantum field theory, we derive the chiral kinetic theory involving
nonlinear quantum corrections coupled with spacetime-dependent electromagnetic
fields and fluid velocity gradients. An equilibrium Wigner function determined
by the kinetic equation verifies the nondissipativeness of the charge induced
by the magneto-vortical coupling. We reveal that this nonlinear chiral kinetic
theory is consistent with the one-loop Euler--Heisenberg effective theory,
indicating an indirect evidence of the trace anomaly in the kinetic theory. We
also argue a potential issue on the regularization, and demonstrate the
availability of the point-splitting regularization in the nonlinear chiral
kinetic theory.
