Article (Scientific journals)
Natural and projectively equivariant quantizations by means of Cartan connections
Mathonet, Pierre; Radoux, Fabian
2005In Letters in Mathematical Physics, 72, p. 183-196
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Keywords :
Quantization; Cartan connections; Projective structures
Abstract :
[en] The existence of a natural and projectively equivariant quantization in the sense of Lecomte was proved recently by M. Bordemann, using the framework of Thomas-Whitehead connections. We give a new proof of existence using the notion of Cartan projective connections and we obtain an explicit formula in terms of these connections. Our method yields the existence of a projectively equivariant quantization if and only if an sl(m+1,R)-equivariant quantization exists in the flat situation, thus solving one of the problems left open by M. Bordemann.
Disciplines :
Mathematics
Author, co-author :
Mathonet, Pierre ;  Université de Liège - ULiège > Département de mathématique > Département de mathématique
Radoux, Fabian ;  Université de Liège - ULiège > Département de mathématique > Géométrie et théorie des algorithmes
Language :
English
Title :
Natural and projectively equivariant quantizations by means of Cartan connections
Publication date :
2005
Journal title :
Letters in Mathematical Physics
ISSN :
0377-9017
eISSN :
1573-0530
Publisher :
Springer Science & Business Media B.V., Dordrecht, Netherlands
Volume :
72
Pages :
183-196
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 31 March 2011

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