Equivariant quantization of orbifolds
arXiv:1001.4640 · doi:10.1016/j.geomphys.2010.04.003
Abstract
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... In this work, we prove 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 \cite{PoRaWo}. 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.
13 pages
References in corpus (8)
- Sur l'existence d'une prescription d'ordre naturelle projectivement invariante
- Natural and projectively equivariant quantizations by means of Cartan Connections
- Projectively equivariant symbol calculus
- Maximal subalgebras of vector fields for equivariant quantizations
- Equivariant symbol calculus for differential operators acting on forms
- Projectively equivariant quantization and symbol calculus: noncommutative hypergeometric functions
- Classical phase space singularities and quantization
- A First Approximation for Quantization of Singular Spaces