We derive a quantum kinetic theory for fermions with arbitrary mass in a background electromagnetic field using a Wigner-function approach. Since spin of massive fermions is a dynamical degree of freedom (d.o.f.), kinetic equations with leading-order quantum corrections describe entangled dynamics of not only vector- and axial-charge distributions but also of the spin polarization. Therefore, we obtain one scalar and one axial-vector kinetic equations with magnetization currents pertinent to the spin-orbit interaction. We show that our results smoothly reduce to the massless limit where the spin of massless fermions is no longer an independent dynamical d.o.f. but is enslaved by the chirality and momentum, and the accordingly kinetic equations turn into chiral kinetic theory for Weyl fermions. We provide a kinetic theory covering both massive and massless cases and hence resolving the problem of constructing a bridge between them. Such a generalization may be crucial for applications to various physical systems. Based on our kinetic equations, we discuss the anomalous currents transported by massive fermions in thermal equilibrium.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)