A first approximation for quantization of singular spaces |
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Authors: | Norbert Poncin Fabian Radoux Robert Wolak |
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Institution: | 1. University of Luxembourg, Campus Limpertsberg, Institute of Mathematics, 162A, avenue de la Faïencerie, L-1511 Luxembourg City, Luxembourg;2. Jagiellonian University, ulica Reymonta 4 30-059 Krakow, Poland |
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Abstract: | 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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Keywords: | 53D50 53C12 53B10 53D20 |
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