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Existence of Natural and Projectively Equivariant Quantizations

S. Hansoul
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Abstract

We study the existence of natural and projectively equivariant quantizations for differential operators acting between order 1 vector bundles over a smooth manifold M. To that aim, we make use of the Thomas-Whitehead approach of projective structures and construct a Casimir operator depending on a projective Cartan connection. We attach a scalar parameter to every space of differential operators, and prove the existence of a quantization except when this parameter belongs to a discrete set of resonant values.

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S. Hansoul. 2006-01-21. Existence of Natural and Projectively Equivariant Quantizations. https://arxiv.org/abs/math/0601518

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