A Remark on Non-equivalent Star Products via Reduction for CP^n

Details A Remark on Non-equivalent Star Products via Reduction for CP^n A Remark on Non-equivalent Star Products via Reduction for CP^n

1998-02-17

arxiv.org/abs/math/9802078v1

Mathematics

Quantum Algebra

7 pages, LaTeX 2e

Scientific paper

In this paper we construct non-equivalent star products on CP^n by phase space reduction. It turns out that the non-equivalent star products occur very natural in the context of phase space reduction by deforming the momentum map of the U(1)-action on C^{n+1} {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 CP^n are obtained by this construction.

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