Moyal quantization with compact symmetry groups and noncommutative harmonic analysis

DOI10.1063/1.528967zbMath0753.43002OpenAlexW1975797303MaRDI QIDQ4713349

Héctor Figueroa, Joseph C. Várilly, José M. Gracia-Bondía

Publication date: 25 June 1992

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.528967

zbMATH Keywords

density matricessymmetry groupscoadjoint orbitsquantum mechanicstwisted productWigner functionsspecial functionMoyal quantizationcompact connected semisimple Lie groupsphase-space variablesharmonic analysis on compact groups

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Applications of Lie groups to the sciences; explicit representations (22E70) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. (43A30) Analysis on other specific Lie groups (43A80)

Related Items (20)

The Stratonovich–Weyl correspondence for one-dimensional kinematical groups ⋮ Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations ⋮ Coherent states, quantum gravity, and the Born- Oppenheimer approximation. II. Compact Lie groups ⋮ Symbolic calculus on the nilpotent orbits of \(SO_ 0(1,2)\) ⋮ Equipartition of the eigenfunctions of quantized ergodic maps on the torus ⋮ Moyal quantization of 2+1-dimensional Galilean systems ⋮ Stratonovich-Weyl correspondence for compact semisimple Lie groups ⋮ Quantization of the affine group of a local field ⋮ GeneralizedSU(2) covariant Wigner functions and some of their applications ⋮ Wigner function for the orientation state ⋮ ON THE ⋆-PRODUCT QUANTIZATION AND THE DUFLO MAP IN THREE DIMENSIONS ⋮ The complex Weyl calculus as a Stratonovich-Weyl correspondence for the real diamond group ⋮ On phase-space representations of quantum mechanics ⋮ FUZZY COMPLEX GRASSMANNIAN SPACES AND THEIR STAR PRODUCTS ⋮ Unnamed Item ⋮ Invariant symbolic calculus for compact Lie groups ⋮ Unnamed Item ⋮ Geometrical origin of the \(\ast\)-product in the Fedosov formalism ⋮ Coherent states and Berezin quantization for non-scalar holomorphic representations ⋮ SU(1, 1) covariant s-parametrized maps

Cites Work

• General concept of quantization
• The Moyal representation for spin
• Some ideas about quantization
• Deformation theory and quantization. I: Deformations of symplectic structures
• Deformation quantization of Heisenberg manifolds
• The characters of unitary representations of Lie groups
• Relativistic quantum kinematics in the Moyal representation
• Fourier analysis on compact symmetric space
• On the Quantum Correction For Thermodynamic Equilibrium

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