  Starting from the density-matrix equation of motion, we derive a
semiclassical kinetic equation for a general two-band electronic Hamiltonian,
systematically including quantum-mechanical corrections up to second order in
space-time gradients. We find, in addition to band-projected corrections to the
single-particle equation of motion due to phase-space Berry curvature,
interband terms that we attribute to the nonorthorgonality of the projected
Hilbert spaces. As examples, we apply our kinetic equation to electronic
systems in the presence of spatially inhomogeneous and dynamical spin textures
stemming from electromagnetic gauge potentials. Specifically, we consider the
electromagnetic response of massive two-dimensional Dirac fermions and
three-dimensional Weyl fermions, and reproduce the anomalous currents known as
the parity and the Adler-Bell-Jackiw anomaly in particle physics.
