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We demonstrate the emergence of the magnetic moment and spin-vorticitycoupling of chiral fermions in 4-dimensional Wigner functions. In linearresponse theory with space-time varying electromagnetic fields, the parity-oddpart of the electric conductivity can also be derived which reproduces resultsof the one-loop and the hard-thermal or hard-dense loop. All these propertiesshow that the 4-dimensional Wigner functions capture comprehensive aspects ofphysics for chiral fermions in electromagnetic fields.

Magnetic moment, vorticity-spin coupling and parity-odd conductivity of chiral fermions in 4-dimensional Wigner functions