  We derive the topological Chern number of the integer quantum Hall effect in
electrical conductivity, using Buot's superfield and lattice Weyl transform
nonequilibrium quantum transport formalism. The method is naturally
straightforward, appropriate for treating nonequilibrium systems acted on by
external electromagnetic fields. We have identified the topological invariant
in the effective (~p; ~q; E; t)-phase space via the nonequilibrium quantum
transport equation, generally not to first-order in electric field but to
first-order in the gradient expansion. We have also derive the Kubo
current-current correlation for the Hall current as a by-product of our new
transport approach. The Berry curvature related to orbital magnetic moment is
also calculated.
