  We study the Keldysh Green's function of the Weyl-fermion surface state of
the three-dimensional topological insulator coupled with a space-time dependent
magnetization in the gradient expansion. Based on it we analyze the electric
charge and current densities as well as the energy density and current induced
by spatially and temporally slowly-varying magnetization fields. We show that
all the above quantities except the energy current are generated by the
emergent electromagnetic fields. The energy current emerges as the circular
current reflecting the spatial modulation of an induced gap of the Weyl
fermion.
