  We present a general quantum kinetic theory of low-field magnetotransport in
weakly disordered crystals that accounts fully for the interplay between
electric-field induced interband coherence, Bloch-state scattering, and an
external magnetic field. The quantum kinetic equation we derive for the
Bloch-state density matrix naturally incorporates the momentum-space Berry
phase effects whose influence on Bloch-state wavepacket dynamics is normally
incorporated into transport theory in an ad hoc manner. The Berry phase
correction to the momentum-space density of states in the presence of an
external magnetic field implied by semiclassical wavepacket dynamics is
captured by our theory as an intrinsic density-matrix response to a magnetic
field. We propose a simple and general procedure for expanding the linear
response of the Bloch-state density matrix to an electric field in powers of
magnetic field. As an illustration, we apply our theory to magnetotransport in
Weyl semimetals. We show that the chiral anomaly (positive magnetoconductivity
quadratic in magnetic field) that appears when separate Fermi surface pockets
surround distinct Weyl points survives only when intervalley scattering is very
weak compared to intravalley scattering.
