A REMARK ON NONEQUIVALENT STAR PRODUCTS VIA REDUCTION FOR CPN

In this Letter, we construct nonequivalent star products on CPn by pha se space reduction. It turns out that the nonequivalent star products occur very natural in the context of phase space reduction by deformin g the momentum map of the U(1)-action on Cn+1\[O] into a quantum momen tum map and the corresponding momentum value into a quantum momentum v alue such that the level set, i.e. the 'constraint surface', of the qu antum momentum map coincides with the classical one. All equivalence c lasses of star products on CPn are obtained by this construction.