  Integral quantum Hall plateau transitions in a planar lattice system due to
gap collapse can be described by an effective field theory with Dirac fermions.
We discuss how to reproduce the correct integral values for the Hall
conductance, $\sigma_{xy}$, before and after the plateau transition, which are
dictated by the microscopic topological invariant. In addition to the massless
Dirac fermions that appear at gap closing, the matching condition of
$\sigma_{xy}$ requires the introduction of massive Dirac fermions, as
"spectators", in the effective field theory. For non-interacting electrons on
the lattice, we give a general prescription to determine these massive
"spectators", based on microscopic information on the vortices in the magnetic
Brillouin zone which are closely related to edge states. Our description is
demonstrated in a model with both nearest-neighbor and next-nearest-neighbor
hoppings.
