General Noncommuting Curvilinear Coordinates and Fluid Mechanics
S. A. Alavi
Department of Physics, Sabzevar University of Tarbiat Moallem, Sabzevar, PO Box 397, Iran
Sabzevar House of Physics, Asrar Laboratories of Physics, Laleh Square, Sabzevar, Iran
General Noncommuting Curvilinear Coordinates and Fluid Mechanics
S. A. Alavi
Department of Physics, Sabzevar University of Tarbiat Moallem, Sabzevar, PO Box 397, Iran
Sabzevar House of Physics, Asrar Laboratories of Physics, Laleh Square, Sabzevar, Iran
Abstract： We show that restricting the states of a charged particle to the lowest Landau level introduces noncommutativity between general curvilinear coordinate operators. The Cartesian, circular cylindrical and spherical polar coordinates are three special cases of our quite general method. The connection between U(1) gauge fields defined on a general noncommuting curvilinear coordinates and fluid mechanics is explained. We also recognize the Seiberg--Witten map from general noncommuting to commuting variables as the quantum correspondence of the Lagrange-to-Euler map in fluid mechanics.
S. A. Alavi. General Noncommuting Curvilinear Coordinates and Fluid Mechanics[J]. 中国物理快报, 2006, 23(10): 2637-2639.
S. A. Alavi. General Noncommuting Curvilinear Coordinates and Fluid Mechanics. Chin. Phys. Lett., 2006, 23(10): 2637-2639.
2006, Vol. 23 
