Existence of Natural and Projectively Equivariant Quantizations

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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.
27 pages, 5 figures

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Differential Geometry, 58A05, 53B05, 46L65, 58J70

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http://salesiana.dossiersoluciones.com/handle/123456789/107643

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0601518
 http://arxiv.org/abs/math/0601518

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arXiv