Variations on deformation quantization

Abstract

I have chosen, in this presentation of Deformation Quantization, to focus on 3 points: the uniqueness --up to equivalence-- of a universal star product (universal in the sense of Kontsevich) on the dual of a Lie algebra, the cohomology classes introduced by Deligne for equivalence classes of differential star products on a symplectic manifold and the construction of some convergent star products on Hermitian symmetric spaces. Those subjects will appear in a promenade through the history of existence and equivalence in deformation quantization.

Text of my talk at the Moshe Flato conference in Dijon in September 1999

References in corpus (6)

• Another proof of M. Kontsevich formality theorem
• Homogeneous Fedosov Star Products on Cotangent Bundles I: Weyl and Standard Ordering with Differential Operator Representation
• Quantization of Poisson algebraic groups and Poisson homogeneous spaces
• Questions on quantization
• A star-product approach to noncompact quantum groups
• Quantization of Poisson structures on ${\mathbb{R}}^2$

Cited by in corpus (23)

• Quantization Methods: A Guide for Physicists and Analysts
• Deformation quantization in the teaching of quantum mechanics
• The characteristic classes of Morita equivalent star products on symplectic manifolds
• Universality of Fedosov's Construction for Star Products of Wick Type on Pseudo-Kähler Manilfolds
• The Picard groupoid in deformation quantization
• Traces for star products on the dual of a Lie algebra
• Formal Deformations of Dirac Structures
• Semiclassical Geometry of Quantum Line Bundles and Morita Equivalence of Star Products
• Convergent Star Products for Projective Limits of Hilbert Spaces
• Deformation Quantization of Hermitian Vector Bundles
• Deformation Quantization: Observable Algebras, States and Representation Theory
• Noncommutative field theories from a deformation point of view
• Some Remarks on {$\mathfrak{g}$}-invariant Fedosov Star Products and Quantum Momentum Mappings
• The natural definition of the quantum dynamical entropy in the framework of deformation quantization
• Invariant Star Products of Wick Type: Classification and Quantum Momentum Mappings
• Classical limit of the Kepler problem and the contraction of phase space
• Morita equivalence of Fedosov star products and deformed Hermitian vector bundles
• Convergence of the Wick Star Product
• The Deformation Quantization of $\Real^n$ via the specifiaction of the commutators
• Formal deformations of Poisson structures in low dimensions
• Bohr-Sommerfeld Star Products
• The Covariant Picard Groupoid in Differential Geometry
• The H-Covariant Strong Picard Groupoid