Area Preserving Transformations in Non-commutative Space and NCCS Theory

Abstract

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.

revtex, 9 pages, corrected typos

References in corpus (6)

• Quantum Field Theory on Noncommutative Spaces
• The Quantum Hall Fluid and Non-Commutative Chern Simons Theory
• Physical Instances of Noncommuting Coordinates
• Covariant Coordinate Transformations on Noncommutative Space
• Noncommuting fields and non-Abelian fluids
• Geometric Transformations and NCCS Theory in the Lowest Landau Level

Cited by in corpus (1)

• On the NCCS model of the quantum Hall fluid