  We demonstrate the emergence of the magnetic moment and spin-vorticity
coupling of chiral fermions in 4-dimensional Wigner functions. In linear
response theory with space-time varying electromagnetic fields, the parity-odd
part of the electric conductivity can also be derived which reproduces results
of the one-loop and the hard-thermal or hard-dense loop. All these properties
show that the 4-dimensional Wigner functions capture comprehensive aspects of
physics for chiral fermions in electromagnetic fields.
