q-deformed Star Products and Moyal Brackets

Abstract

The standard and anti-standard ordered operators acting on two-dimensional q-deformed phase space are shown to satisfy algebras which can be called W_\infty. q-star products and q-Moyal brackets corresponding to these algebras are constructed. Some applications like defining q-classical mechanics and q-path integrals are discussed.

12 pages, latex, minor changes and refs. added

References in corpus (9)

• Infinite Symmetry in the Quantum Hall Effect
• Fermions in the Lowest Landau Level: Bosonization, $W_{\infty }$ Algebra, Droplets, Chiral Boson
• Conformal Symmetry and Universal Properties of Quantum Hall States
• Area-preserving diffeomorphisms, W_{\infty} and $U_{q}(sl(2)) in Chern-Simons theory and Quantum Hall system
• Infinite Symmetry in the Fractional Quantum Hall Effect
• Q-Deformed Path Integral
• $s{l}_q(2)$ Realizations for Kepler and Oscillator Potentials and q-Canonical Transformations
• On the deformability of Heisenberg algebras
• Non-Commutative Geometry on Quantum Phase-Space