Bargmann-Fock sheaves on Kähler manifolds

Abstract

Fedosov used flat sections of the Weyl bundle on a symplectic manifold to construct a star product $\star$ which gives rise to a deformation quantization. By extending Fedosov's method, we give an explicit, analytic construction of a sheaf of Bargmann-Fock modules over the Weyl bundle of a Kähler manifold $X$ equipped with a compatible Fedosov abelian connection, and show that the sheaf of flat sections forms a module sheaf over the sheaf of deformation quantization algebras defined $(C_X^{\infty }[[\hslash ]],\star )$. This sheaf can be viewed as the $\hslash$-expansion of $L^{\otimes k}$ as $k\to \infty$, where $L$ is a prequantum line bundle on $X$ and $\hslash =1/k$.

27 pages; v2: published version

References in corpus (2)

• Tropical Lagrangian multi-sections and smoothing of locally free sheaves over degenerate Calabi-Yau surfaces
• Kapranov's $L_{\infty }$ structures, Fedosov's star products, and one-loop exact BV quantizations on Kähler manifolds

Cited by in corpus (3)

• Quantization of Kähler manifolds
• Quantizable functions on Kähler manifolds and non-formal quantization
• Geometric quantization and quantum moment maps on coadjoint orbits and Kähler-Einstein manifolds