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.

We compute the momentum diffusion coefficients of heavy quarks, ${\kappa }_{\parallel }$ and ${\kappa }_{\perp }$, in a strong magnetic field $B$ along the directions parallel and perpendicular to $B$, respectively, at the leading order in QCD coupling constant ${\alpha }_s$. We consider a regime relevant for the relativistic heavy ion collisions, ${\alpha }_{s}eB\ll T^2\ll eB$, so that thermal excitations of light quarks are restricted to the lowest Landau level (LLL) states. In the vanishing light-quark mass limit, we find ${\kappa }_{\perp }^{\mathrm{LO}}\propto {\alpha }_s^{2}TeB$ in the leading order that arises from screened Coulomb scatterings with ($1+1$)-dimensional LLL quarks, while ${\kappa }_{\parallel }$ gets no contribution from the scatterings with LLL quarks due to kinematic restrictions. We show that the first nonzero leading order contributions to ${\kappa }_{\parallel }^{\mathrm{LO}}$ come from the two separate effects: (1) the screened Coulomb scatterings with thermal gluons, and (2) a finite light-quark mass $m_q$. The former leads to ${\kappa }_{\parallel }^{\mathrm{LO},\text{gluon}}\propto {\alpha }_s^2{T}^3$ and the latter to ${\kappa }_{\parallel }^{\mathrm{LO},\text{massive}}\propto {\alpha }_s({\alpha }_{s}eB{)}^{1/2}{m}_q^2$. Based on our results, we propose a new scenario for the large value of heavy-quark elliptic flow observed in RHIC and LHC. Namely, when ${\kappa }_{\perp }\gg {\kappa }_{\parallel }$, an anisotropy in drag forces gives rise to a sizable amount of the heavy-quark elliptic flow even if heavy quarks do not fully belong to an ellipsoidally expanding background fluid.

We compute the electrical conductivity of quark-gluon plasma in a strong magnetic field $B$ with quantum field theory at finite temperature using the lowest Landau level approximation. We provide the one-loop result arising from 1-to-2 scattering processes of which the kinematics are satisfied by the ($1+1$)-dimensional fermion dispersion relation. Because of the chirality conservation, the conductivity diverges in the massless limit and is sensitive to the value of the current quark mass. As a result, we find that the conductivity along the direction of the magnetic field is quite large compared with the value at $B=0$, mainly because of the small value of the current quark mass. We show that the resummation of the ladder diagrams for the current-current correlator gives rise to only subleading contributions beyond the leading-log order and thus verify our one-loop result at the leading-log accuracy. We also discuss possible implications for the relativistic heavy-ion collisions.

We systematically derive the collision term for the axial kinetic theory, a quantum kinetic theory delineating the coupled dynamics of the vector/axial charges and spin transport carried by the massive spin-1/2 fermions traversing a medium. We employ the Wigner-function approach and propose a consistent power-counting scheme where the axial-charge distribution function, a non-conserved quantity for massive particles, is accounted as the first-order quantity in the ħ expansion, while the vector-charge distribution function the zeroth-order quantity. This specific power-counting scheme allows us to organize a reduced ħ expansion for the collision term and to formally identity the spin- diffusion effect and the spin-polarization effect at the same order. We confirm that the obtained collisional axial kinetic theory smoothly reduces to the chiral kinetic theory in the massless limit, serving as a consistency check. In the absence of electromagnetic fields, we further present the simplified axial kinetic equations suitable for tracking dynamical spin polarization of heavy and light fermions, respectively. As an application to the weakly coupled quark-gluon plasma at high temperature, we compute the spin-diffusion term for massive quarks within the leading-log approximation. The formal expression for the first- order terms provides a path toward evaluation of the spin polarization effect in quantum chromodynamics.