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We derive a semi-classical effective action and the kinetic equation formassive Dirac fermions in electromagnetic fields. The non-Abelian Berry phasestructure emerges from two helicity states of massive fermions with positiveenergy. The classical spin emerges as a vector in SU(2) helicity space. Thecontinuity equations for the fermion number and the classical spin are derived.The fermion number is conserved while the spin charge is not conserved byanomaly. Previous results about the coefficients of the chiral magnetic effectfor the fermion and axial currents in the chiral limit can be reproduced afterincluding the anti-fermion contributions. This provides an example for theemerging spin and non-Abelian Berry phase of Dirac fermions arising from thefermion mass.

Kinetic equations for massive Dirac fermions in electromagnetic field with non-Abelian Berry phase