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arXiv · 2003.06732

A new construction of strict deformation quantization for Lagrangian fiber bundles

Mayuko Yamashita
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Abstract

We give a new construction of strict deformation quantization of symplectic manifolds equipped with a proper Lagrangian fiber bundle structure, whose representation spaces are the quantum Hilbert spaces obtained by geometric quantization. The construction can be regarded as a "lattice approximation of the correspondence between differential operators and principal symbols". We analyze the corresponding formal deformation quantization. We also investigate into relations between our construction and Berezin-Toeplitz deformation quantization.

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Mayuko Yamashita. 2020-03-15. A new construction of strict deformation quantization for Lagrangian fiber bundles. https://arxiv.org/abs/2003.06732

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