Reference : Equivariant quantization of orbifolds
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Equivariant quantization of orbifolds
Poncin, Norbert mailto [University of Luxembourg > Unité de Recherche en Mathématiques > > Professor >]
Radoux, Fabian mailto [Université de Liège - ULiège > Département de mathématique > Géométrie et théorie des algorithmes >]
Wolak, Robert mailto [Jagiellonian University > > > Professor >]
Journal of Geometry & Physics
Yes (verified by ORBi)
[en] Equivariant quantization, singular quantization, singular geometric object, orbifold, foliated manifold, desingularization
[en] Equivariant quantization is a new theory that highlights the role of symmetries in the relationship between classical and quantum dynamical systems. These symmetries are also one of the reasons for the recent interest in quantization of singular spaces, orbifolds, stratified spaces, etc. In this work, we prove the existence of an equivariant quantization for orbifolds. Our construction combines an appropriate desingularization of any Riemannian orbifold by a foliated smooth manifold, with the foliated equivariant quantization that we built in Poncin et al. (2009) [19]. Further, we suggest definitions of the common geometric objects on orbifolds, which capture the nature of these spaces and guarantee, together with the properties of the mentioned foliated resolution, the needed correspondences between singular objects of the orbifold and the respective foliated objects of its desingularization.
Fonds de la Recherche Scientifique (Communauté française de Belgique) - F.R.S.-FNRS

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