Spectral convergence in geometric quantization -- the case of non-singular Langrangian fibrations

Kota Hattori; Mayuko Yamashita

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arXiv · 1912.07994

Spectral convergence in geometric quantization -- the case of non-singular Langrangian fibrations

Kota Hattori·Mayuko Yamashita

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Abstract

We develop a new approach to geometric quantization using the theory of convergence of metric measure spaces. Given a family of K\"ahler polarizations converging to a non-singular real polarization on a prequantized symplectic manifold, we show the spectral convergence result of $\bar{\partial}$-Laplacians, as well as the convergence result of quantum Hilbert spaces. We also consider the case of almost K\"ahler quantization for compatible almost complex structures, and show the analogous convergence results.

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BibTeX RIS

Kota Hattori, Mayuko Yamashita. 2019-12-17. Spectral convergence in geometric quantization -- the case of non-singular Langrangian fibrations. https://arxiv.org/abs/1912.07994

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