Berezin-Toeplitz quantization on symplectic manifolds of bounded geometry

TL;DR

This paper develops Berezin-Toeplitz quantization for symplectic manifolds with bounded geometry, demonstrating that it correctly captures the semiclassical limit through spectral analysis of the Bochner Laplacian.

Contribution

It extends Berezin-Toeplitz quantization theory to symplectic manifolds of bounded geometry, linking quantum spaces to spectral subspaces of the Bochner Laplacian.

Findings

Quantum space corresponds to spectral subspace of Bochner Laplacian

Quantization exhibits correct semiclassical limit

Framework applicable to manifolds of bounded geometry

Abstract

We establish the theory of Berezin-Toeplitz quantization on symplectic manifolds of bounded geometry. The quantum space of this quantization is the spectral subspace of the renormalized Bochner Laplacian associated with some interval near zero. We show that this quantization has the correct semiclassical limit.