Subalgebras with converging star products in deformation quantization: An algebraic construction for C P n

DOI10.1063/1.531779zbMath0923.58024arXivq-alg/9512019OpenAlexW2002950452MaRDI QIDQ5284694

C. Emmrich, M. Brischle, Stefan Waldmann, Martin Bordemann

Publication date: 31 October 1999

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

Full work available at URL: https://arxiv.org/abs/q-alg/9512019

zbMATH Keywords

deformation quantizationconverging star products

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 selfadjoint operator algebras to physics (46L60) Geometry and quantization, symplectic methods (81S10) General mathematical topics and methods in quantum theory (81Q99) Applications of functional analysis in quantum physics (46N50) Geometric quantization (53D50)

Related Items (11)

Deformation quantization of surjective submersions and principal fibre bundles ⋮ Symmetry reduction of states. II: A non-commutative positivstellensatz for \(\mathbb{C} \mathbb{P}^n\) ⋮ Wick rotations in deformation quantization ⋮ Symmetry reduction of states. I ⋮ STATES AND REPRESENTATIONS IN DEFORMATION QUANTIZATION ⋮ Algebraic Rieffel induction, formal Morita equivalence, and applications to deformation quantization. ⋮ Fuzzy complex projective spaces and their star-products ⋮ A convergent star product on the Poincaré disc ⋮ Group actions in deformation quantization ⋮ Homogeneous Fedosov star products on cotangent bundles. II: GNS representations, the WKB expansion, traces, and applications ⋮ Comparison and continuity of Wick-type star products on certain coadjoint orbits

Cites Work

• Existence of star-products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds
• Weyl manifolds and deformation quantization
• Deformation theory and quantization. I: Deformations of symplectic structures
• Quantization of Kähler manifolds. III
• Covariant deformations on polarized orbits of a Lie group
• \(gl(\infty{})\) and geometric quantization
• *-products on some Kähler manifolds
• Quantization of Kähler manifolds. IV
• Phase space reduction for star-products: An explicit construction for \(\mathbb{C} P^ n\)
• Quantization of Kähler manifolds. I: Geometric interpretation of Berezin's quantization
• COHERENT STATES AND KAHLER MANIFOLDS

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