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Quantum moment maps and invariants for G-invariant star products

Kentaro Hamachi
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Abstract

We study a quantum moment map and propose an invariant for $G$-invariant star products on a $G$-transitive symplectic manifold. We start by describing a new method to construct a quantum moment map for $G$-invariant star products of Fedosov type. We use it to obtain an invariant that is invariant under $G$-equivalence. In the last section we give two simple examples of such invariants, which involve non-classical terms and provide new insights into the classification of $G$-invariant star products.

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Kentaro Hamachi. 2002-03-20. Quantum moment maps and invariants for G-invariant star products. https://doi.org/10.1142/s0129055x02001314

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