  Motivated by a recent proposal on the possibility of observing a monopole in
the band structure, and by an increasing interest on the role of Berry phase in
spintronics, we studied the adiabatic motion of a wave packet of Bloch
functions, under a perturbation varying slowly and incommensurately to the
lattice structure. We show using only the fundamental principles of quantum
mechanics that its effective wave-packet dynamics is conveniently described by
a set of equations of motion (EOM) for a semiclassical particle coupled to a
nonabelian gauge field associated with a geometric Berry phase. Our EOM can be
viewed as a generalization of the standard Ehrenfest's theorem, and their
derivation was asymptotically exact in the framework of linear response theory.
Our analysis is entirely based on the concept of local Bloch bands, a good
starting point for describing the adiabatic motion of a wave packet. One of the
advantages of our approach is that the various types of gauge fields were
classified into two categories by their different physical origin: (i)
projection onto specific bands, (ii) time-dependent local Bloch basis. Using
those gauge fields, we write our EOM in a covariant form, whereas the
gauge-invariant field strength stems from the noncommutativity of covariant
derivatives along different axes of the reciprocal parameter space. The
degeneracy of Bloch bands makes the gauge fields nonabelian. We applied our
formalism to the analyses on various types of Hall and polarization currents.
We highlighted their behavior under time reversal (T) and space inversion (I).
The concept of parity polarization current was also introduced. Together with
charge/spin Hall/polarization currents, this type of orbital current is
expected to be a potential probe for detecting and controling Berry phase.
