Using derivative expansion applied to the Wigner transform of the two - point
Green function we analyse the anomalous quantum Hall effect (AQHE), and the
chiral magnetic effect (CME). The corresponding currents are proportional to
the momentum space topological invariants. We reproduce the conventional
expression for the Hall conductivity in $2+1$ D. In $3+1$ D our analysis allows
to explain systematically the AQHE in topological insulators and Weyl
semimetals. At the same time using this method it may be proved, that the
equilibrium CME is absent in the wide class of solids, as well as in the
properly regularized relativistic quantum field theory.Comment: Latex, 26 page
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