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

Louis Ioos; Wen Lu; Xiaonan Ma; George Marinescu

doi:10.1007/s12220-017-9977-y

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

Louis Ioos, Wen Lu, Xiaonan Ma^*, George Marinescu

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	2615-2646
Number of pages	32
Journal	Journal of Geometric Analysis
Volume	30
Issue number	3
DOIs	https://doi.org/10.1007/s12220-017-9977-y
State	Published - 1 Jul 2020
Externally published	Yes

Keywords

Berezin-Toeplitz quantization
Bochner Laplacian
Generalized Bergman kernel
Toeplitz operator

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10.1007/s12220-017-9977-y

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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.",

keywords = "Berezin-Toeplitz quantization, Bochner Laplacian, Generalized Bergman kernel, Toeplitz operator",

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AU - Marinescu, George

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AB - 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.

KW - Berezin-Toeplitz quantization

KW - Bochner Laplacian

KW - Generalized Bergman kernel

KW - Toeplitz operator

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

Abstract

Keywords

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