Existence of a closed star product

DOI10.1007/BF00420238zbMath0771.58017MaRDI QIDQ1803241

Akira Yoshioka, Hideki Omori, Yoshiaki Maeda

Publication date: 29 June 1993

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

zbMATH Keywords

symplectic manifoldclosed star productdeformation of the Poisson algebraWeyl diffeomorphism

Mathematics Subject Classification ID

Noncommutative topology (46L85) Noncommutative differential geometry (46L87) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items

Observables of angular momentum as observables on the Fedosov quantized sphere, Star products on compact pre-quantizable symplectic manifolds, Some continuous field quantizations, equivalent to the \(C^*\)-Weyl quantization, DEFORMATION QUANTIZATION: IS C₁ NECESSARILY SKEW?, Deformational quantization of Poisson structures, Berezin-Toeplitz quantization for compact Kähler manifolds. A review of results, Quantization: Deformation and/or functor?, Quantization on a two-dimensional phase space with a constant curvature tensor., Berezin-Toeplitz quantization and naturally defined star products for Kähler manifolds, An explicit formula for the Berezin star product, Geometrical origin of the \(\ast\)-product in the Fedosov formalism, Quantization of emergent gravity, Traces for star products on symplectic manifolds

Cites Work

• Existence of star-products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds
• Weyl manifolds and deformation quantization
• Closed star products and cyclic cohomology
• Deformation theory and quantization. I: Deformations of symplectic structures
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