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Berezin–Toeplitz Quantization on Symplectic Manifolds of Bounded Geometry

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Abstract

The theory of Berezin–Toeplitz quantization on symplectic manifolds of bounded geometry is developed. The quantization space is a suitable eigenspace of the renormalized Bochner operator associated with a neighborhood of zero. It is proved that quantization has a correct semiclassical limit.

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Funding

This work was carried out in the framework of the development program of the Scientific-Educational Mathematical Center of Volga Federal District (agreement no. 075-02-2020-1478).

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Authors and Affiliations

  1. Institute of Mathematics with Computing Center of Ufa Federal Research Center of Russian Academy of Sciences, Ufa, 450008, Russia

    Yu. A. Kordyukov

  2. Kazan (Volga Region) Federal University, Kazan, 420008, Russia

    Yu. A. Kordyukov

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  1. Yu. A. Kordyukov
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Correspondence to Yu. A. Kordyukov.

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Translated from Matematicheskie Zametki, 2022, Vol. 112, pp. 586–600 https://doi.org/10.4213/mzm13731.

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Kordyukov, Y.A. Berezin–Toeplitz Quantization on Symplectic Manifolds of Bounded Geometry. Math Notes 112, 576–587 (2022). https://doi.org/10.1134/S0001434622090267

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  • DOI: https://doi.org/10.1134/S0001434622090267

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