  Statistical average of the axial current is evaluated on the basis of the
covariant Wigner function. In the resulting formula, chemical potential $\mu$,
angular velocity $\Omega$ and acceleration $a$ enter in combination $\mu \pm
(\Omega \pm ia)/2$. The limiting cases of zero mass and zero temperature are
investigated in detail. In the zero-mass limit, the axial current is described
by a smooth function only at temperatures higher than the Unruh temperature. At
zero temperature, the axial current, as a function of the angular velocity and
chemical potential, vanishes in a two-dimensional plane region.
