A geometric construction of representations of the Berezin-Toeplitz quantization

Abstract

For a Kähler manifold $X$ equipped with a prequantum line bundle $L$, we give a geometric construction of a family of representations of the Berezin-Toeplitz deformation quantization algebra $(C^{\infty }(X)[[\hslash ]],{\star }_{BT})$ parametrized by points $z_0\in X$. The key idea is to use peak sections to suitably localize the Hilbert spaces $H^0\left(X,L^{\otimes m}\right)$ around $z_0$ in the large volume limit.

28 pages, 1 figure; v3: published version

References in corpus (1)

• Lectures on Batalin-Vilkovisky formalism and its applications in topological quantum field theory

Cited by in corpus (2)

• Quantization of Kähler manifolds
• Kapranov's $L_{\infty }$ structures, Fedosov's star products, and one-loop exact BV quantizations on Kähler manifolds