A New Invariant For G-Invariant Star Products

Abstract

The purpose of this Letter is to propose an invariant for a G-invariant star product on a G-transitive symplectic manifold which remains invariant under the G-equivalence maps. This invariant is defined by using a quantum moment map which is a quantum analogue of the moment map on a Hamiltonian G-space. On S2 regarded as an SO(3) coadjoint orbit in \( \mathfrak{s}\mathfrak{o}\left( 3 \right)* \), we give an example of this invariant for the canonical G-invariant star product. In this example, there arises a nonclassical term which depends only on a class of G-invariant star products.