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 : https://doi.org/10.5802/aif.2517
Classification : 53D50
Mots clés : quantification géométrique, système intégrable, singularité non-dégénérée
@article{AIF_2010__60_1_51_0,
     author = {Hamilton, Mark D. and Miranda, Eva},
     title = {Geometric quantization of integrable systems with hyperbolic singularities},
     journal = {Annales de l'Institut Fourier},
     pages = {51--85},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {60},
     number = {1},
     year = {2010},
     doi = {10.5802/aif.2517},
     mrnumber = {2664310},
     zbl = {1191.53058},
     language = {en},
     url = {www.numdam.org/item/AIF_2010__60_1_51_0/}
}
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/item/AIF_2010__60_1_51_0/

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