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A remark on nonequivalent star products via reduction for \(\mathbb{C}\mathbb{P}^n\). (English) Zbl 0924.58119
Summary: We construct nonequivalent star products on \(\mathbb{C}\mathbb{P}^n\) by phase space reduction. It turns out that the nonequivalent star products occur very natural in the context of phase space reduction by deforming the momentum map of the U(1)-action on \(\mathbb{C}^{n-1}\setminus\{0\}\) into a quantum momentum map and the corresponding momentum value into a quantum momentum value such that the level set, i.e., the ‘constraint surface’, of the quantum momentum map coincides with the classical one. All equivalence classes of star products on \(\mathbb{C}\mathbb{P}^n\) are obtained by this construction.

MSC:
58H15 Deformations of general structures on manifolds
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics
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