  Starting from a general $N$-band Hamiltonian with weak spatial and temporal
variations, we derive a low energy effective theory for transport within one or
several overlapping bands. To this end, we use the Wigner representation that
allows us to systematically construct the unitary transformation that brings
the Hamiltonian into band-diagonal form. We address the issue of gauge
invariance and discuss the necessity of using kinetic variables in order to
obtain a low energy effective description that is consistent with the original
theory. Essentially, our analysis is a semiclassical one and quantum
corrections appear as Berry curvatures in addition to quantities that are
related to the appearance of persistent currents. We develop a transport
framework which is manifestly gauge invariant and it is based on a quantum
Boltzman formulation along with suitable definitions of current density
operators such that Liouville's theorem is satisfied. Finally, we incorporate
the effects of an external electromagnetic field into our theory.
