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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 |
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| Cite this article: |
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S. A. Alavi 2006 Chin. Phys. Lett. 23 2637-2639 |
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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.
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| Keywords:
02.40.Gh
03.65.-w
02.20.-a
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Published: 01 October 2006
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