Geometric quantization of integrable systems with hyperbolic singularities
Annales de l'Institut Fourier, Volume 60 (2010) no. 1, pp. 51-85.

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.

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.

DOI: 10.5802/aif.2517
Classification: 53D50
Keywords: Geometric quantization, integrable system, non-degenerate singularity
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, Volume 60 (2010) no. 1, pp. 51-85. doi : 10.5802/aif.2517. https://aif.centre-mersenne.org/articles/10.5802/aif.2517/

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