Geometric quantization of integrable systems with hyperbolic singularities
[Quantification géométrique des systèmes intégrables avec singularités hyperboliques]
Annales de l'Institut Fourier, Tome 60 (2010) no. 1, pp. 51-85.

On construit la quantification géométrique d’une surface compacte en utilisant une polarisation singulière donnée par un système intégrable. Cette polarisation présente toujours des singularités qu’on suppose de type non-dégénéré. En particulier, on calcule l’effet des singularités hyperboliques qui donnent une contribution de dimension infinie à la quantification, en démontrant que cette quantification dépend fortement de la polarisation choisie.

We construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. In particular, we compute the effect of hyperbolic singularities, which make an infinite-dimensional contribution to the quantization, thus showing that this quantization depends strongly on polarization.

DOI : 10.5802/aif.2517
Classification : 53D50
Keywords: Geometric quantization, integrable system, non-degenerate singularity
Mot clés : quantification géométrique, système intégrable, singularité non-dégénérée
Hamilton, Mark D. 1 ; Miranda, Eva 2

1 Graduate School of Mathematical Sciences University of Tokyo 3-8-1 Komaba Meguro-Ku Tokyo 153-8914 (Japan)
2 Universitat Autònoma de Barcelona 08193 Bellaterra (Spain)
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Hamilton, Mark D.; Miranda, Eva. Geometric quantization of integrable systems with hyperbolic singularities. Annales de l'Institut Fourier, Tome 60 (2010) no. 1, pp. 51-85. doi : 10.5802/aif.2517. http://www.numdam.org/articles/10.5802/aif.2517/

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