Existence of Natural and Projectively Equivariant Quantizations
Differential Geometry
2007-05-23 v1
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.
Cite
@article{arxiv.math/0601518,
title = {Existence of Natural and Projectively Equivariant Quantizations},
author = {S. Hansoul},
journal= {arXiv preprint arXiv:math/0601518},
year = {2007}
}
Comments
27 pages, 5 figures