Kinetic theory with spin: From massive to massless fermions

Abstract

We find that the recently developed kinetic theories with spin for massive and massless fermions are smoothly connected. By introducing a reference-frame vector, we decompose the dipole-moment tensor into electric and magnetic dipole moments. We show that the axial-vector component of the Wigner function contains a contribution from the transverse magnetic dipole moment, which accounts for the transverse spin degree of freedom (d.o.f.) and vanishes smoothly in the massless limit. As a result, the kinetic equations, describing 4 d.o.f. for massive fermions, smoothly becomes the chiral kinetic equations describing 2 d.o.f. in the massless limit. We also confirm the small-mass behavior of the Wigner function by an explicit calculation using a Gaussian wave packet.