Phase space reduction for star-products: An explicit construction for CPn

We derive a closed formula for a star-product on complex projective space and on the domain SU(n+1)/S(U(1)xU(n)) using a completely elementary construction: Starting from the standard star-product of Wick type on C-n+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 C-n+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)x(n)).