Reference : Natural and projectively equivariant quantizations by means of Cartan connections
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/88063
Natural and projectively equivariant quantizations by means of Cartan connections
English
Mathonet, Pierre mailto [Université de Liège - ULiège > Département de mathématique > Département de mathématique >]
Radoux, Fabian mailto [Université de Liège - ULiège > Département de mathématique > Géométrie et théorie des algorithmes >]
2005
Letters in Mathematical Physics
Springer Science & Business Media B.V.
72
183-196
Yes (verified by ORBi)
International
0377-9017
Dordrecht
The Netherlands
[en] Quantization ; Cartan connections ; Projective structures
[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.
Researchers
http://hdl.handle.net/2268/88063
10.1007/s11005-005-6783-4

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