  We develop the quantum Boltzman equation approach for the Kondo breakdown
quantum critical point, involved with two bands for conduction electrons and
localized fermions. Particularly, the role of vertex corrections in transport
is addressed, crucial for non-Fermi liquid transport of temperature linear
dependence. Only one band of spinons may be considered for scattering with
gauge fluctuations, and their associated vertex corrections are introduced in
the usual way, where divergence of self-energy corrections is cancelled by that
of vertex corrections, giving rise to the physically meaningful result in the
gauge invariant expression for conductivity. On the other hand, two bands
should be taken into account for scattering with hybridization excitations,
giving rise to coupled quantum Boltzman equations. We find that vertex
corrections associated with hybridization fluctuations turn out to be
irrelevant due to heavy mass of spinons in the so called decoupling limit,
consistent with the diagrammatic approach showing the non-Fermi liquid
transport.
