Quantum moment maps and invariants for G-invariant star products

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.

20 pages

Cited by in corpus (3)

• Natural star products on symplectic manifolds and quantum moment maps
• Classification of Equivariant Star Products on Symplectic Manifolds
• Characteristic classes of star products on Marsden-Weinstein reduced symplectic manifolds