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arXiv · 2601.06619

Families of Toeplitz operators, family index and deformation quantization

Clément Cren·Erfan Rezaei
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Abstract

Given a contact fibration, we construct smooth families of Szeg\"o projections on the fibers. This allows us to define smooth families of Toeplitz operators. We apply these operators to construct a deformation quantization of prequantizable symplectic fibrations, recovering a result of Kravchenko in an analytic way. We also derive a family index for these families of Toeplitz operators. To this end, we generalize an index formula of Baum and van Erp to families.

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Clément Cren, Erfan Rezaei. 2026-01-10. Families of Toeplitz operators, family index and deformation quantization. https://arxiv.org/abs/2601.06619

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