Axial Kinetic Theory and Spin Transport for Fermions with Arbitrary Mass

Abstract

We derive the quantum kinetic theory for fermions with arbitrary mass in a background electromagnetic field from the Wigner-function approach. Since spin of massive fermions is a dynamical degree of freedom, the kinetic equations with the leading-order quantum corrections describe entangled dynamics of not only the 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 degree of freedom but is enslaved by the chirality and momentum and the accordingly kinetic equations turn into the chiral kinetic theory for Weyl fermions. We provide a kinetic theory covering both the massive and massless cases, and hence resolves the problem in constructing the bridge between them. Such 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.