  We apply the Wigner-function approach and chiral kinetic theory to
investigate the angular momentum and polarization of chiral fluids composed of
Weyl fermions with background electric/magnetic fields and vorticity. It is
found that the quantum corrections in Wigner functions give rise to nonzero
anti-symmetric components in the canonical energy-momentum tensors, which are
responsible for the spin-orbit interaction. In global equilibrium, conservation
of the canonical angular momentum reveals the cancellation between the orbital
component stemming from side jumps with nonzero vorticity and the spin
component in the presence of an axial chemical potential. We further analyze
the conservation laws near local equilibrium. It turns out that the canonical
angular momentum is no longer conserved even in the absence of background
fields due to the presence of a local torque coming from the spin-orbit
interaction involving temperature/chemical-potential gradients, which is
implicitly led by collisions.
