Geometric quantization of integrable systems with hyperbolic singularities
[Quantification géométrique des systèmes intégrables avec singularités hyperboliques]
Hamilton, Mark D. ; Miranda, Eva
Annales de l'Institut Fourier, Tome 60 (2010), p. 51-85 / Harvested from Numdam

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.

Publié le : 2010-01-01
DOI : https://doi.org/10.5802/aif.2517
Classification:  53D50
Mots clés: quantification géométrique, système intégrable, singularité non-dégénérée
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     author = {Hamilton, Mark D. and Miranda, Eva},
     title = {Geometric quantization of integrable systems with hyperbolic singularities},
     journal = {Annales de l'Institut Fourier},
     volume = {60},
     year = {2010},
     pages = {51-85},
     doi = {10.5802/aif.2517},
     zbl = {1191.53058},
     mrnumber = {2664310},
     language = {en},
     url = {http://dml.mathdoc.fr/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) pp. 51-85. doi : 10.5802/aif.2517. http://gdmltest.u-ga.fr/item/AIF_2010__60_1_51_0/

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