Berezin–Toeplitz Quantization for Eigenstates of the Bochner Laplacian on Symplectic Manifolds

Abstract

We study the Berezin–Toeplitz quantization using as quantum space the space of eigenstates of the renormalized Bochner Laplacian corresponding to eigenvalues localized near the origin on a symplectic manifold. We show that this quantization has the correct semiclassical behavior and construct the corresponding star-product.