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Morita equivalence of Fedosov star products and deformed Hermitian vector bundles. (English) Zbl 1009.53063
From the author’s abstract: The usual Fedosov construction of star products for a symplectic manifold \(M\) [B. V. Fedosov, Deformation Quantization and Index Theory, Akademie Verlag, Berlin (1996; Zbl 0867.58061)] is adapted in order to give a simple geometric construction of a bimodule deformation for the sections of a vector bundle \(E\) over \(M\) starting with a symplectic torsion-free connection on \(M\) and a connection for \(E\). In the case of a line bundle, this gives a Morita equivalence bimodule and the relation between the characteristic classes of the Morita equivalent star products can be found easily. In the case of a Hermitian vector bundle, the author gives a Fedosov construction of the deformation of the Hermitian fiber metric.

MSC:
53D55 Deformation quantization, star products
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