AREA PRESERVING DIFFEOMORPHISM, QUANTUM GROUP AND BERRY PHASE

Abstract

We study here the relationship between the area preserving diffeomorphism and quantum group with the deformation of symplectic structure and Berry phase in the Landau problem of 2D electron gas in a magnetic field. It is argued that while the area preserving diffeomorphism leads to the quantization of the symmetry [Formula: see text], the deformation of the symplectic structure leads to the quantization of the system having the relation Δp. Δ q=2πnℏ, n being an odd integer giving rise to the Berry phase ei2πμ with n=2μ. A possible link between the deformation parameter q of the deformed algebra [Formula: see text] with the Berry phase factor arising out of the quantization procedure has been suggested. Finally, the latticization of space associated with the quantum group and its connection with the Zp spin system is discussed.