  For an isotropic single-band system, it is well known that the semiclassical
Boltzmann transport theory within the relaxation time approximation and the
Kubo formula with the vertex corrections provide the same result with the
$(1-\cos\theta)$ factor in the inverse transport relaxation time. In
anisotropic multiband systems, the semiclassical Boltzmann transport equation
is generalized to coupled integral equations relating transport relaxation
times at different angles in different bands. Using the Kubo formula, we study
the vertex corrections to the dc conductivity in anisotropic multiband systems
and derive the relation satisfied by the transport relaxation time for both
elastic and inelastic scatterings, verifying that the result is consistent with
the semiclassical approach.
