## 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 $$\mathbb{C}^{n + 1} \backslash \{0\}$$.

### MSC:

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

### Keywords:

star-product; Marsden-Weinstein reduction; Wick product
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### References:

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