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The equations of motion for the position and gauge invariant crystal momentumare considered for multiband wave packets of Bloch electrons. For a localizedpacket in a subset of bands well-separated from the rest of the band structureof the crystal, one can construct an effective electromagnetic Hamiltonian withrespect to the center of the packet. We show that the equations of motion canbe obtained via a projection operator procedure, which is derived from theadiabatic approximation within perturbation theory. These relations explicitlycontain information from each band captured in the expansion coefficients andenergy band structure of the Bloch states as well as non-Abelian featuresoriginating from interband Berry phase properties. This general and transparentHamiltonian-based approach is applied to a wave packet spread over a singleband, a set of degenerate bands, and two linear crossing bands. The generalizedequations of motion hold promise for novel effects in transport currents andHall effect phenomena.

Multiband Effects in Equations of Motion of Observables Beyond the Semiclassical Approach