Reference : A first approximation for quantization of singular spaces
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
A first approximation for quantization of singular spaces
Poncin, Norbert mailto [University of Luxembourg > Unité de Recherche en Mathématiques > > Professor >]
Radoux, Fabian mailto [Université de Liège - ULg > Département de mathématique > Géométrie et théorie des algorithmes >]
Wolak, Robert mailto [Jagiellonian University (Krakow) - JU > > > Professor >]
Journal of Geometry & Physics
Elsevier Science
Yes (verified by ORBi)
The Netherlands
[en] Quantization; Singular space; Reduction; Foliation; Equivariant symbol calculus
[en] Many mathematical models of physical phenomena that have been proposed in recent years require more general spaces than manifolds. When taking into account the symmetry group of the model, we get a reduced model on the (singular) orbit space of the symmetry group action. We investigate quantization of singular spaces obtained as leaf closure spaces of regular Riemannian foliations on compact manifolds. These contain the orbit spaces of compact group actions and orbifolds. Our method uses foliation theory as a desingularization technique for such singular spaces. A quantization procedure on the orbit space of the symmetry group–that commutes with reduction–can be obtained from constructions which combine different geometries associated with foliations and new techniques originated in Equivariant Quantization. The present paper contains the first of two steps needed to achieve these just detailed goals.

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