Article (Scientific journals)
Existence of natural and conformally invariant quantizations of arbitrary symbols
Mathonet, Pierre; Radoux, Fabian
2010In Journal of Nonlinear Mathematical Physics, 17, p. 539-556
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Keywords :
Conformally equivariant quantization; Existence
Abstract :
[en] A quantization can be seen as a way to construct a differential operator with prescribed principal symbol. The map from the space of symbols to the space of differential operators is moreover required to be a linear bijection. In general, there is no natural quantization procedure, that is, spaces of symbols and of differential operators are not equivalent, if the action of local diffeomorphisms is taken into account. However, considering manifolds endowed with additional structures, one can seek for quantizations that depend on this additional structure and that are natural if the dependence with respect to the structure is taken into account. The existence of such a quantization was proved recently in a series of papers in the context of projective geometry. Here, we show that the construction of the quantization based on Cartan connections can be adapted from projective to pseudo-conformal geometry to yield the natural and conformally invariant quantization for arbitrary symbols, outside some critical situations.
Disciplines :
Mathematics
Author, co-author :
Mathonet, Pierre ;  University of Luxembourg > FSTC > Mathematics research unit
Radoux, Fabian ;  Université de Liège - ULiège > Département de mathématique > Géométrie et théorie des algorithmes
Language :
English
Title :
Existence of natural and conformally invariant quantizations of arbitrary symbols
Publication date :
2010
Journal title :
Journal of Nonlinear Mathematical Physics
ISSN :
1402-9251
Publisher :
Atlantis Press, Lulea, Sweden
Volume :
17
Pages :
539-556
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 31 March 2011

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