An explicit formula for the natural and conformally invariant quantization

Abstract

In [5], P. Lecomte conjectured the existence of a natural and conformally invariant quantization. In [7], we gave a proof of this theorem thanks to the theory of Cartan connections. In this paper, we give an explicit formula for the natural and conformally invariant quantization of trace-free symbols thanks to the method used in [7] and to tools already used in [8] in the projective setting. This formula is extremely similar to the one giving the natural and projectively invariant quantization in [8].

12 pages

References in corpus (2)

• Invariant Bilinear Differential Pairings on Parabolic Geometries
• Explicit formula for the natural and projectively equivariant quantization

Cited by in corpus (5)

• Higher Symmetries of the Laplacian via Quantization
• On conformal higher spins in curved background
• Second Order Symmetries of the Conformal Laplacian
• Projectively equivariant quantizations over the superspace ${\mathbb{R}}^{p|q}$
• Conformal geometry of the supercotangent and spinor bundles