Semiclassical Geometry of Quantum Line Bundles and Morita Equivalence of Star Products

Abstract

In this paper we show how deformation quantization of line bundles over a Poisson manifold $M$ produces a canonical action $\Phi$ of the Picard group $\Pic(M)\cong H^2(M,\mathbb Z)$ on the moduli space of equivalence classes of differential star products on $M$, $\Def(M)$. The orbits of $\Phi$ characterize Morita equivalent star products on $M$. We describe the semiclassical limit of $\Phi$ in terms of the characteristic classes of star products by studying the semiclassical geometry of deformed line bundles.

arXiv comment23 pages. Minor corrections made (Sec. 2.1), few typos fixed. Final version to appear at Internat. Math. Res. Notices

References in corpus (5)

• Morita equivalence and duality
• Geometry of the transport equation in multicomponent WKB approximations
• The characteristic classes of Morita equivalent star products on symplectic manifolds
• Variations on deformation quantization
• Noncommutative line bundle and Morita equivalence

Cited by in corpus (7)

• The characteristic classes of Morita equivalent star products on symplectic manifolds
• Poisson geometry and Morita equivalence
• The Picard groupoid in deformation quantization
• Morita equivalence and characteristic classes of star products
• Morita classes of microdifferential algebroids
• Twist star products and Morita equivalence
• Topics in Noncommutative Geometry