Letters in Mathematical Physics

, 89:249

An Explicit Formula for the Natural and Conformally Invariant Quantization


DOI: 10.1007/s11005-009-0335-2

Cite this article as:
Radoux, F. Lett Math Phys (2009) 89: 249. doi:10.1007/s11005-009-0335-2


Lecomte (Prog Theor Phys Suppl 144:125–132, 2001) conjectured the existence of a natural and conformally invariant quantization. In Mathonet and Radoux (Existence of natural and conformally invariant quantizations of arbitrary symbols, math.DG 0811.3710), 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 Mathonet and Radoux and to tools already used in Radoux [Lett Math Phys 78(2):173–188, 2006] in the projective setting. This formula is extremely similar to the one giving the natural and projectively invariant quantization in Radoux.

Mathematics Subject Classification (2000)

53B05 53A30 53D50 53C10 


conformal Cartan connections differential operators natural maps quantization maps 

Copyright information

© Springer 2009

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of LiègeLiègeBelgium

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