An Explicit Formula for the Natural and Conformally Invariant Quantization

Radoux, Fabian

doi:10.1007/s11005-009-0335-2

Download

Article (Scientific journals)

An Explicit Formula for the Natural and Conformally Invariant Quantization

Radoux, Fabian

2009 • In Letters in Mathematical Physics, 89, p. 249-263

Peer Reviewed verified by ORBi

Permalink
https://hdl.handle.net/2268/88041

DOI
10.1007/s11005-009-0335-2

Files (1)Send to Details Statistics Bibliography Similar publications

Files

Full Text

Trace-free.pdf

Author postprint (181.69 kB)

Download

All documents in ORBi are protected by a user license.

Send to

RIS BibTex APA Chicago Permalink X Linkedin

Details

Keywords :

Conformally equivariant quantization; Explicit formula

Abstract :

[en] 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.

Disciplines :

Mathematics

Author, co-author :

Radoux, Fabian ; Université de Liège - ULiège > Département de mathématique > Géométrie et théorie des algorithmes

Language :

English

Title :

An Explicit Formula for the Natural and Conformally Invariant Quantization

Publication date :

2009

Journal title :

Letters in Mathematical Physics

ISSN :

0377-9017

eISSN :

1573-0530

Publisher :

Springer Science & Business Media B.V., Dordrecht, Netherlands

Volume :

Pages :

249-263

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 31 March 2011

Statistics

Number of views

44 (3 by ULiège)

Number of downloads

139 (1 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

Bibliography

Bordemann, M.: Sur l'existence d'une prescription d'ordre naturelle projectivement invariante, math.DG/0208171.
Bouarroudj S.: Formula for the projectively invariant quantization on degree three. C. R. Acad. Sci. Paris Sér. I Math. 333(4), 343-346 (2001).
Čap A., Slovák J., Souček V.: Invariant operators on manifolds with almost Hermitian symmetric structures. I. Invariant differentiation. Acta Math. Univ. Comenian. (N.S.) 66(1), 33-69 (1997).
Duval C., Lecomte P., Ovsienko V.: Conformally equivariant quantization: existence and uniqueness. Ann. Inst. Fourier (Grenoble) 49(6), 1999-2029 (1999).
Duval C., Ovsienko V.: Conformally equivariant quantum Hamiltonians. Selecta Math. (N.S.) 7(3), 291-320 (2001).
Duval C., Ovsienko V.: Projectively equivariant quantization and symbol calculus: noncommutative hypergeometric functions. Lett. Math. Phys. 57(1), 61-67 (2001).
Eastwood M.: Higher symmetries of the Laplacian. Ann. Math. (2) 161(3), 1645-1665 (2005).
Kobayashi, S.: Transformation Groups in Differential Geometry. Springer, New York, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 70 (1972).
Kroeske, J.: Invariant bilinear differential pairings on parabolic geometries. Thesis, School of Pure Mathematics, University of Adelaide, June (2008).
Lecomte, P.B.A.: Towards projectively equivariant quantization. Prog. Theor. Phys. Suppl. 144:125-132 (2001). Noncommutative geometry and string theory (Yokohama, 2001).
Lecomte P.B.A., Ovsienko V.Yu.: Projectively equivariant symbol calculus. Lett. Math. Phys. 49(3), 173-196 (1999).
Mathonet P., Radoux F.: Cartan connections and natural and projectively equivariant quantizations. Lond. Math. Soc. 76, 87-104 (2007).
Mathonet, P., Radoux, F.: Existence of natural and conformally invariant quantizations of arbitrary symbols. math.DG 0811.3710.
Radoux F.: Explicit formula for the natural and projectively equivariant quantization. Lett. Math. Phys. 78(2), 173-188 (2006).