  It is found that the extra quantum constraints to the spinor components of
the equal-time Wigner function given in a recent paper by Zhuang and Heinz
should vanish identically. We point out here the origin of the error and give
an interpretation of the result. However, the principal idea of obtaining a
complete equal-time transport theory by energy averaging the covariant theory
remains valid. The classical transport equation for the spin density is also
found to be incorrect. We give here the correct form of that equation and
discuss briefly its structure.
