Extended Voros product in the coherent states framework

Abstract

Using coherent states of the Weyl-Heisenberg algebra $h_N$, extended Voros products and Moyal brakets are derived. The covariance of Voros product under canonical transformations is discussed. Star product related to Barut-Girardello coherent states of the Lie algebra $su(1,1)$ is also considered. The star eigenvalue problem of singular harmonic osillator is investigated.

References in corpus (13)

• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• Noncommutative Open String and D-brane
• Alternative commutation relations, star products and tomography
• Coherent State Induced Star-Product on $R_{\lambda }^3$ and the Fuzzy Sphere
• Noncommutative Yang-Mills from equivalence of star products
• Generalized Coherent State Approach to Star Products and Applications to the Fuzzy Sphere
• The noncommutative harmonic oscillator in more than one dimensions
• Analytic representations based on SU(1,1) coherent states and their applications
• Generating All Wigner Functions
• Moyal Brackets in M-Theory
• A New Class of Two-Dimensional Noncommutative Spaces
• The Moyal Bracket in the Coherent States framework
• Deformation Quantization of Geometric Quantum Mechanics

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• Duality symmetry for star products
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• Coherent state quantization of angle, time, and more irregular functions and distributions