Area preserving transformationsin non-commutative space and NCCS theory
Department of Theoretical Physics, A. Razmadze Mathematical Institute, M. Aleksidze 1, 380093, Tbilisi , Georgia
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We propose a heuristic rule for the area transformation on the non-commutative plane. The non-commutative area preserving transformations are quantum deformations of the classical symplectic diffeomorphisms. The area preservation condition is formulated as a field equation in the non-commutative Chern-Simons gauge theory. A higher-dimensional generalization is suggested and the corresponding algebraic structure - the infinite-dimensional sin-Lie algebra - is extracted. As an illustrative example the second-quantized formulation for electrons in the lowest Landau level is considered.
© Springer-Verlag, 2003