Abstract
We derive a closed formula for a star-product on complex projective space and on the domain SU(n+1)/S(U(1)×U(n)) using a completely elementary construction: Starting from the standard starproduct of Wick type on ℂn+1\{0} and performing a quantum analogue of Marsden-Weinstein reduction, we can give an easy algebraic description of this star-product. Moreover, going over to a modified star-product on ℂn+1\{0}, obtained by an equivalence transformation, this description can be even further simplified, allowing the explicit computation of a closed formula for the star-product on ℂPn which can easily be transferred to the domain SU(n+1)/S(U(1)×(n)).
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Bordemann, M., Brischle, M., Emmrich, C. et al. Phase space reduction for star-products: An explicit construction for ℂPn . Lett Math Phys 36, 357–371 (1996). https://doi.org/10.1007/BF00714403
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DOI: https://doi.org/10.1007/BF00714403