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Quantification conformément équivariante des fibrés supercotangents

Abstract : This thesis is divided into two parts.
1. Conformally equivariant quantization of supercotangent bundles.
We mean by quantization of the supercotangent bundle of a manifold M, a linear isomorphism between the space of superfunctions, fiberwise polynomial, and the space of differential operators acting on spinors over M. In the case of conformally flat manifolds (M,g), we prove the existence and uniqueness of such a quantization, demanding equivariance with respect to the action of conformal transformations of M.
2. On the projective geometry of the supercircle: a unified construction of the super cross-ratio and Schwarzian derivative.
We establish, for three supergroups acting on the supercircle, a correspondence between the supergroup, the caracteristic invariants of its action and the associated 1-cocycle, defining so three geometries on the supercircle. The caracteristic invariant of the projective geometry is the super cross-ratio, whose 1-cocycle is the Schwarzian derivative.
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Contributor : Jean-Philippe Michel <>
Submitted on : Thursday, October 22, 2009 - 11:54:58 AM
Last modification on : Thursday, September 13, 2018 - 12:08:03 PM
Long-term archiving on: : Thursday, June 17, 2010 - 5:28:36 PM


  • HAL Id : tel-00425576, version 1



Jean-Philippe Michel. Quantification conformément équivariante des fibrés supercotangents. Physique mathématique [math-ph]. Université de la Méditerranée - Aix-Marseille II, 2009. Français. ⟨tel-00425576⟩



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