  The anomalous Hall effect (AHE) is a consequence of spin-orbit coupling in a
ferromagnetic metal and is related primarily to density-matrix response to an
electric field that is off-diagonal in band index. For this reason disorder
contributions to the AHE are difficult to treat systematically using a
semi-classical Boltzmann equation approach, even when weak localization
corrections are disregarded. In this article we explicitly demonstrate the
equivalence of an appropriately modified semiclassical transport theory which
includes anomalous velocity and side jump contributions and microscopic
Kubo-Streda perturbation theory, with particular unconventional contributions
in the semiclassical theory identified with particular Feynman diagrams when
calculations are carried out in a band-eigenstate representation. The
equivalence we establish is verified by explcit calculations for the case of
the two-dimensional (2D) Dirac model Hamiltonian relevant to graphene.
