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Berezin-Toeplitz quantization for eigenstates of the Bochner-Laplacian on symplectic manifolds

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arxiv 1703.06420 v1 pith:HG2JI3KF submitted 2017-03-19 math.DG

Louis Ioos , Wen Lu , Xiaonan Ma , George Marinescu This is my paper · ORCID
classification math.DG
keywords quantizationberezin-toeplitzcorrespondingeigenstatesspacesymplecticbehaviorbochner
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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.

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  1. Semiclassical eigenvalue asymptotics for the Bochner Laplacian of a positive line bundle on a symplectic manifold

    math.SP 2019-08 accept novelty 6.0 of 10

    On a closed symplectic manifold, the low-lying eigenvalues of the Bochner Laplacian on L^p are pτ0 + μj + O(p^{-1/2}), where μj are eigenvalues of model Toeplitz operators at the wells.

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