Recently, the anomalous transport of Weyl fermions such as the renowned chiral magnetic effect stemming from the chiral anomaly has been widely studied in relativistic heavy ion collisions, Weyl semimetals, or even in astrophysics. Although such anomalous transport is in general non-dissipative and independent of couplings in thermal equilibrium, the non-equilibrium (or near-equilibrium) transport of Weyl fermions could be affected by other quantum effects and interactions. The chiral kinetic theory (CKT), which delineates quasi-particle transport with the chiral anomaly, is a useful tool to investigate quantum transport in and out of equilibrium for Weyl-fermion systems at weak coupling. In this talk, I will review the recent development of CKT based on quantum field theories, which manifests Lorentz covariance and consistently incorporates collisions. We then apply the CKT to study second-order quantum transport of chiral fluids near local equilibrium. By using a relaxation-time approximation, novel anomalous Hall currents pertinent to interactions and triggered by electric fields and temperature/chemical-potential gradients are discovered. Moreover, the chiral magnetic/vortical effects receive viscous corrections. In addition, one finds that the CKT yields a non-vanishing antisymmetric component of the canonical energy-momentum tensor in chiral fluids with vorticity, which reveals the spin-orbit interaction responsible for angular-momentum transfer in the presence of an axial chemical potential.

References :
Di-Lun Yang, arXiv:1807.02395
Yoshimasa Hidaka, Di-Lun Yang, Phys.Rev. D98 (2018) no.1, 016012, arXiv:1801.08253
Yoshimasa Hidaka, Shi Pu, Di-Lun Yang , Phys. Rev. D 97 (2018) no.1, 016004, arXiv:1710.00278
Yoshimasa Hidaka, Shi Pu, Di-Lun Yang , Phys.Rev. D95 (2017) no.9, 091901, (Rapid Communication), arXiv:1612.04630