Covariance and geometrical invariance in *quantization

DOI10.1063/1.525703zbMath0515.22015OpenAlexW2059831974MaRDI QIDQ3661831

Didier Arnal, Paul Molin, Georges Pinczon, J. C. Cortet

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1063/1.525703

zbMATH Keywords

invariancedeformationPoisson bracketcovariancestar productcommutation rulesphase-spaceWeyl-Wigner quantizationfinite dimensional Lie algebra of observablessymplectic, connected, paracompact manifold

Mathematics Subject Classification ID

Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Applications of Lie groups to the sciences; explicit representations (22E70) Lie algebras of Lie groups (22E60) Representations of Lie algebras and Lie superalgebras, analytic theory (17B15)

Related Items (24)

*-products in the method of orbits for nilpotent groups ⋮ Classification of equivariant star products on symplectic manifolds ⋮ The \(H\)-covariant strong Picard groupoid ⋮ Covariant deformations on polarized orbits of a Lie group ⋮ On the symplectic structure of coadjoint orbits of (solvable) Lie groups and applications. I ⋮ Covariant star-products ⋮ Geometric Quantization and The Universal Enveloping Algebra of a Nilpotent Lie Group ⋮ Deformations of momentum maps and G-systems ⋮ Contractions of Lie algebras with 2-dimensional generic coadjoint orbits ⋮ Star-products and phase space realizations of quantum groups ⋮ Application of the star-product method to the angular momentum quantization ⋮ Orderings and non-formal deformation quantization ⋮ Invariant star products of Wick type: classification and quantum momentum mappings ⋮ Involutions and representations for reduced quantum algebras ⋮ Some remarks on \(\mathfrak g\)-variant Fedosov star products and quantum momentum mappings ⋮ Symbolic calculus on the time-frequency half-plane ⋮ Poisson algebras and transverse structures ⋮ Nilpotent Fourier transform and applications ⋮ Group actions in deformation quantization ⋮ Geometrical origin of the \(\ast\)-product in the Fedosov formalism ⋮ Homogeneous Fedosov star products on cotangent bundles. II: GNS representations, the WKB expansion, traces, and applications ⋮ Représentations \({}^*\) des groupes exponentiels. \((^*\)- representations of exponential groups) ⋮ Star representations of E(2) ⋮ Invariant star-products on symplectic manifolds

Cites Work

• Some ideas about quantization
• Déformation du crochet de Poisson sur une variété symplectique
• Deformation theory and quantization. I: Deformations of symplectic structures

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