The Moyal Bracket in the Coherent States framework

Abstract

The star product and Moyal bracket are introduced using the coherent states corresponding to quantum systems with non-linear spectra. Two kinds of coherent state are considered. The first kind is the set of Gazeau-Klauder coherent states and the second kind are constructed following the Perelomov-Klauder approach. The particular case of the harmonic oscillator is also discussed.

13 pages

References in corpus (11)

• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• Noncommutative Open String and D-brane
• D-branes and the Noncommutative Torus
• f-Oscillators and Nonlinear Coherent States
• Temporally stable coherent states for infinite well and Pöschl-Teller potentials
• Generalized Coherent State Approach to Star Products and Applications to the Fuzzy Sphere
• Analytic representations based on SU(1,1) coherent states and their applications
• Coherent states à la Klauder-Perelomov for the Pöschl-Teller potentials
• Generalized Intelligent States for an Arbitrary Quantum System
• Generalized Intelligent States for Nonlinear Oscillators
• Dual D-Brane Actions on $Ad{S}^5\times S^5$

Cited by in corpus (5)

• Photon-added coherent states for exactly solvable Hamiltonians
• Statistical properties of Klauder-Perelomov coherent states for the Morse potential
• Extended Voros product in the coherent states framework
• Generalized coherent states for q-oscillator connected with q-Hermite polynomials
• Covariance of noncommutative Grassmann star product