Phase space reduction for star-products: An explicit construction for \(\mathbb{C} P^ n\)
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Publication:1912760
DOI10.1007/BF00714403zbMath0849.58035arXivq-alg/9503004OpenAlexW3106020827MaRDI QIDQ1912760
Stefan Waldmann, M. Brischle, C. Emmrich, Martin Bordemann
Publication date: 14 May 1996
Published in: Letters in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/q-alg/9503004
Geometry and quantization, symplectic methods (81S10) Local differential geometry of Hermitian and Kählerian structures (53B35) Geometric quantization (53D50)
Related Items (23)
Classification of equivariant star products on symplectic manifolds ⋮ Subalgebras with converging star products in deformation quantization: An algebraic construction for C P n ⋮ Gauge theories on noncommutative ℂPN and Bogomol’nyi-Prasad-Sommerfield-like equations ⋮ 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 ⋮ On Gammelgaard's formula for a star product with separation of variables ⋮ QUANTIZATION METHODS: A GUIDE FOR PHYSICISTS AND ANALYSTS ⋮ Gauge theories in noncommutative homogeneous Kähler manifolds ⋮ On dynamical adjoint functor ⋮ Deformation quantization with separation of variables of an endomorphism bundle ⋮ Deformation quantization with separation of variables for complex two-dimensional locally symmetric Kähler manifold ⋮ Symmetry reduction of states. I ⋮ Explicit formula of deformation quantization with separation of variables for complex two-dimensional locally symmetric Kähler manifold ⋮ Noncommutative deformations of locally symmetric Kähler manifolds ⋮ Invariant star products on \(S^2\) and the canonical trace ⋮ Some remarks on \(\mathfrak g\)-variant Fedosov star products and quantum momentum mappings ⋮ A convergent star product on the Poincaré disc ⋮ Comparison and continuity of Wick-type star products on certain coadjoint orbits ⋮ A new noncommutative product on the fuzzy two-sphere corresponding to the unitary representation of SU(2) and the Seiberg-Witten map ⋮ Explicit formulas for noncommutative deformations of ${\mathbb C}{P^N}$CPN and ${\mathbb C}{H^N}$CHN ⋮ Triangular dynamical \(r\)-matrices and quantization ⋮ Fuzzy \({\mathbb C}P^2\).
Cites Work
- Existence of star-products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds
- *-products on \(D^ 1(C)\), \(S^ 2\) and related spectral analysis
- An explicit *-product on the cotangent bundle of a Lie group
- Geodesic symmetries and invariant star products on Kähler symmetric spaces
- Local cohomology of the algebra of \(C^\infty\) functions on a connected manifold
- Lorentz manifolds modelled on a Lorentz symmetric space
- Deformation theory and quantization. I: Deformations of symplectic structures
- Quantization of Kähler manifolds. III
- A simple geometrical construction of deformation quantization
- *-products on some Kähler manifolds
- Quantization of Kahler Manifolds. II
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