Area Preserving Transformations in Non-commutative Space and NCCS Theory

Details Area Preserving Transformations in Non-commutative Space and NCCS Theory Area Preserving Transformations in Non-commutative Space and NCCS Theory

2003-06-25

arxiv.org/abs/hep-th/0306249v2

Eur.Phys.J. C32 (2003) 135-140

Physics

High Energy Physics

High Energy Physics - Theory

revtex, 9 pages, corrected typos

Scientific paper

10.1140/epjc/s2003-01373-3

We propose an heuristic rule for the area transformation on the non-commutative plane. The non-commutative area preserving transformations are quantum deformation of the classical symplectic diffeomorphisms. Area preservation condition is formulated as a field equation in the non-commutative Chern-Simons gauge theory. The 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.

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