Hamiltonian theory of anyons in crystals

Semiclassical wave packets for electrons in crystals, subject to external electromagnetic field, satisfy Hamiltonian equations. In $(2+1)$-dimensions and in the limit of uniform fields, the symmetry group results a two-folded Galilei algebra, incorporating an “exotic” central charge. It has the physical meaning of the Berry-phase curvature. In the Hamiltonian scheme, we discuss possible deformations of that algebra and the physical meaning.