  We develop a formalism for treating coherent wave-packet dynamics of charge
and spin carriers in degenerate and nearly degenerate bands. We consider the
two-band case carefully in view of spintronics applications, where transitions
between spin-split bands often occur even for relatively weak electromagnetic
fields. We demonstrate that much of the semiclassical formalism developed for
the single-band case can be generalized to multiple bands, and examine the
nontrivial non-Abelian corrections arising from the additional degree of
freedom. Along with the center of mass motion in crystal momentum and real
space, one must also include a pseudo-spin to characterize the dynamics between
the bands. We derive the wave packet energy up to the first order gradient
correction and obtain the equations of motion for the real- and $k$-space
center of the wave-packet, as well as for the pseudo-spin. These equations
include the non-Abelian Berry curvature terms and a non-Abelian correction to
the group velocity. As an example, we apply our formalism to describe coherent
wave-packet evolution under the action of an electric field, demonstrating that
it leads to electrical separation of up and down spins. A sizable separation
will be observed, with a large degree of tunability, making this mechanism a
practical method of generating a spin polarization. We then turn our attention
to a magnetic field, where we recover Larmor precession, which cannot be
obtained from a single-band point of view. In this case, the gradient energy
correction can be regarded as due to a magnetic moment from the self-rotation
of the wave-packet, and we calculate its value for the light holes in the
spherical four-band Luttinger model.
