  In this paper we introduce the axial gauge field to the framework of the
quantum kinetic theory with vector gauge field in the massless limit. Treating
axial-gauge field on an equal footing with the vector-gauge field, we construct
a consistent solution to the kinetic equations up to the first order in
gradient expansion or equivalently the semi-classical expansion. The intuitive
extension of quantum kinetic theory presented in this work provides a natural
generalization, and turns out to give rise to the covariant anomaly and the
covariant currents. The corresponding consistent currents can be obtained from
the covariant ones by adding the Chern-Simons current. We use the consistent
currents to calculate various correlation functions among currents and
energy-momentum tensor in equilibrium state.

High Energy Physics - Phenomenology;Mesoscale and Nanoscale Physics;Nuclear Theory