Phase space reduction for star-products: An explicit construction for \(\mathbb{C} P^ n\). (English) Zbl 0849.58035

The authors give an explicit formula for a star-product on the complex projective space and the domain \(SU(1,n)/SU(1) \times U(n)\) which in addition is shown to be the Marsden-Weinstein reduction of a star product equivalent to the usual Wick product on the flat Kähler manifold \(\mathbb{C}^{n + 1} \backslash \{0\}\).


53D50 Geometric quantization
53B35 Local differential geometry of Hermitian and Kählerian structures
81S10 Geometry and quantization, symplectic methods
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