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.
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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